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A toxicity risk assessment method for spill incidents involving volatile liquid hydrocarbons and aqueous solutions in enclosed areas
Journal of Loss Prevention in the Process Industries 23 (2010) 719e726
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A toxicity risk assessment method for spill incidents involving volatile liquid hydrocarbons and aqueous solutions in enclosed areas Nikolaos Kazantzis a, *, Vasiliki Kazantzi b a b
Department of Chemical Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609-2280, USA Department of Project Management, Technological Educational Institute (TEI) of Larissa, Larissa 41110, Greece
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 February 2010 Received in revised form 19 May 2010 Accepted 4 June 2010
A new method for the assessment of toxicity risk due to spill incidents involving volatile liquid hydrocarbons and aqueous solutions in enclosed areas is proposed. First, mass transfer models coupled with time-varying evaporation and emission rates (source models) are used to estimate the dynamic concentration profiles of potentially toxic gas/vapor pollutants resulting from spills of volatile liquid hydrocarbons as well as aqueous solutions in an enclosed area or indoor environment. Recognizing that toxicity risk depends nonlinearly on exposure duration and concentration, while the latter varies dynamically with time at any receptor position, the use of the aforementioned models to reliably compute toxic loads in the presence of time-varying concentration profiles is pursued explicitly in the present study. In this manner, one effectively overcomes the limitations of more traditional approaches to toxicity risk assessment where toxic loads are estimated under constant (steady state, average or mean) concentration levels of the toxic pollutant. Furthermore, instead of resorting to complex physiologically inspired pharmacokinetic models and the associated formidable multi-parameter estimation problems requiring the availability of large sets of good and reliable data, the proposed method incorporates also the idea of using a simple dynamic description that provides the requisite degree of differentiation between the exposure concentration obtained through the above models and the effective concentration (often associated with dose) that reaches the receptor site as determined by the uptake rate of a toxic vapor/gas. On the basis of the timevarying effective concentration or dose, an effective toxic load that takes into account potential recovery processes is then computed and integrated into a probit methodological framework where the proper quantification of a population response to toxic exposure (effective toxic load) provides the means to assess and characterize toxicity risk. Finally, the proposed method is evaluated through simulation studies in a case study involving a spill episode of ammonia solution in an enclosed area. 2010 Elsevier Ltd. All rights reserved.
Keywords: Chemical risk assessment Spill incidents Volatile liquid hydrocarbons Aqueous solutions Time-varying emission rates Toxicity assessment
1. Introduction The quantification of risk assessment associated with incidents involving the natural, accidental or intentional release of potentially hazardous chemicals into the environment has been recognized as a rather useful methodological paradigm and well-justified research endeavor by the scientific community, provided that its inherent limitations and extent of scope are carefully acknowledged in a complex world where uncertainty reigns (Holland & Sielken, 1993; van Leeuwen & Hermens, 1995; Louvar & Louvar, 1997; Ramaswami, Milford, & Small, 2005; Scheringer, 2002; Trapp & Matthies, 1998). In the presence of complexity, quantitative risk models with varying degrees of sophistication should aim at * Corresponding author. Tel.: þ1 508 8315666; fax: þ1 508 8315853. E-mail addresses: [email protected] (N. Kazantzis), [email protected] (V. Kazantzi). 0950-4230/$ e see front matter 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jlp.2010.06.005
complementing and skillfully guiding intuition, which should be also exercised as models aspire to capture even value-laden facets of complex situations (Holland & Sielken, 1993; van Leeuwen & Hermens, 1995; Louvar & Louvar, 1997; Scheringer et al., 2001; Slovic, Finucane, Peters, & MacGregor, 2004). Given: 1) the considerable uncertainties in modeling emission/release conditions, 2) the complexity of the combined effect of inherent physicochemical properties and environmental processes on the fate of a chemical, 3) the physiological responses of individuals to different levels of exposure (notwithstanding the variability within a certain population), and 4) the paucity of reliable data at all the above stages, risk models should not be expected to provide the “right answer” and generate predictions endowed with absolute mathematical precision, but
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instead become useful tools enabling scientists to ask the right questions without resorting to costly experimentation (Holland & Sielken, 1993; Louvar & Louvar, 1997; Ramaswami et al., 2005; Scheringer, 2002; Scheringer et al., 2001; Slovic et al., 2004; van Leeuwen & Hermens, 1995). Indeed, they could be used to: i) identify the sources of uncertainty with the highest impact on risk assessment, and/or ii) identify conditions under which significant risk might occur, and/or iii) form the basis of a reliable risk-informed screening method Therefore, the above quantitative risk assessment methods should allow for (the finite) available resources to be concentrated on and emphasis to be placed on cases where furthermore detailed assessment is needed in order to reduce uncertainty and mitigate/ manage risk (van Leeuwen & Hermens, 1995; Scheringer, 2002; Scheringer et al., 2001). Under this spirit, the present study aims at developing a quantitative framework for the assessment of toxicity risk posed by spill incidents involving volatile liquid hydrocarbons and aqueous solutions in an enclosed area or indoor environment. Following the principles of the conceptual framework presented in (van Leeuwen & Hermens, 1995; Scheringer et al., 2001), one is first reminded that hazard identification is related to the inherent physicochemical properties of the chemical under consideration as well as the occurrence conditions of the spill incident itself. Furthermore, the overall risk is quantitatively represented as the product of the probability of occurrence of the above incident multiplied by the conditional probability of observing a fatality (the health end-point in the present study) due to exposure to toxic vapor given the occurrence of the spill incident. Notice that the second probabilistic term in the overall risk is the term traditionally associated with chemical risk assessment which also captures the effects (or consequences) on public health and/or ecosystem functions (van Leeuwen & Hermens, 1995; Scheringer, 2002; Scheringer et al., 2001). Chemical risk depends explicitly on a measure of exposure or dose which can be in principle estimated through a chemodynamics model that explicitly takes into account the combined effect of inherent physicochemical properties and underlying environmental processes on the fate of the chemical, often in conjunction with a physiologically inspired pharmacokinetic model in order to determine the physiologically important effective dose (Andersen, 2003; Holland & Sielken, 1993; van Leeuwen & Hermens, 1995; Ramaswami et al., 2005; Scheringer, 2002; Trapp & Matthies, 1998). Typically, a quantitative sense of the size or significance of risk is obtained through the notion of risk quotient which is based on a direct comparison of the aforementioned exposure measure or dose to an effect level or threshold concentration such as the Permissible Exposure Limit (PEL) or the Immediately Dangerous to Life and Health Limit (IDLH) (van Leeuwen & Hermens, 1995; Louvar & Louvar, 1997; Ramaswami et al., 2005; Scheringer, 2002; Scheringer et al., 2001). Finally, the extent or consequences of the above risk are quantified through a doseresponse type of relationship such as the one associated with a probit model, which, within the context of the present study, could provide a probabilistic measure of an expected number (or percentage) of fatalities due to exposure to toxic vapor of a certain population (Finney, 1971; Lee, 2002; van Leeuwen & Hermens, 1995; Louvar & Louvar, 1997; Ramaswami et al., 2005; Scheringer et al., 2001). Overcoming some of the limitations associated with existing approaches, the proposed method: i) allows a more realistic time-varying rather than constant evaporation/emission rate to be incorporated into a spill model as in (Guo, 2002; Guo, Sparks, & Roache, 2008) ii) uses explicitly a more realistic description of toxic load resulting from a spill incident as a nonlinear time-varying
dynamic quantity rather than one based on a constant (steady state, average or mean) concentration profile (Lee, 2002), and incorporates it into an appropriate probit model. Indeed, it has been convincingly demonstrated that nonlinear toxic load models generalizing the traditional Haber’s law in toxicology are more suitable to reliably quantify the combined health effect of exposure concentration and exposure time/ duration (ten Berge, Zwart, & Appelman, 1986; Hilderman, Hrudey, & Wilson, 1999; Ride, 1984). In particular, they overcome the limitations of Haber’s law associated with overestimating health responses to low concentrations and large exposure times, as well as underestimating health responses at high concentrations and short exposure times (as in acute toxicity episodes) (Hilderman et al., 1999; Holland & Sielken, 1993; Ride, 1984; ten Berge et al., 1986). Furthermore, the above nonlinear generalizations of Haber’s law profoundly change the effect of time-varying dynamic concentration profiles during the exposure window on health responses compared to constant concentration values (steady state, average or mean) (ten Berge et al., 1986; Hilderman et al., 1999; Ride, 1984), and this should be necessarily taken into account by any reliable chemical risk assessment model for spill incidents. iii motivated by the ideas introduced in the excellent work (Hilderman et al., 1999), bypasses the complexity and challenges that often accompany the development of a comprehensive physiologically based pharmacokinetic model to quantify the physiologically relevant effective concentration or dose available at the receptor site (Andersen, 2003; Holland & Sielken, 1993; Ramaswami et al., 2005). This is achieved by introducing: 1) a simple linear first-order dynamic description with an empirical parameter called the uptake time-constant relating the toxic vapor concentration in the enclosed area calculated through the spill model to the effective concentration (dose) responsible for health effects, and 2) a second linear first-order dynamic description with an empirical parameter called the recovery time-constant that captures underlying physiological recovery processes (metabolic reduction of chemical toxicity in the human body, excretion mechanisms, tissue repair mechanisms, etc). On the basis of the above models, an effective toxic load is then defined and integrated into a probit methodological framework (Finney, 1971; Holland & Sielken, 1993) where the proper quantification of a population response to toxic exposure (effective toxic load) provides the means to assess and characterize toxicity risk. The present paper is organized as follows: Section 2 encompasses the requisite preliminaries associated with spill models involving volatile liquid hydrocarbons and aqueous solutions in an indoor environment, as well as the traditional structure of a probit model for toxicity risk assessment due to exposure to toxic vapor produced by the above spill incidents. The paper’s main results and proposed method are presented in Section 3, followed by its evaluation in a case study discussed in Section 4 focusing on a spill incident of ammonia solution in an enclosed area. Finally, a few concluding remarks are provided in Section 5. 2. Spill models for volatile liquid hydrocarbons and aqueous solutions in enclosed areas As mentioned in the introductory Section 1, the proposed risk assessment method involving spill incidents of volatile liquid hydrocarbons and aqueous solutions relies on the integrated use of an appropriate spill model coupled with a probit model and
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a model for the effective toxic load that explicitly take into account the dynamic time-varying nature of both the emission/evaporation rate and toxic vapor concentration profiles, a physiologically important effective concentration profile at the appropriate receptor site, as well as the nonlinearity of the health response of a population to a particular exposure pattern. At this point, the reader is reminded that modeling within the context of the proposed quantitative toxicity risk assessment methodology is viewed not as a means to provide a level of absolute accuracy and reality capturing capacity in its predictions for an inherently complex phenomenon such as the one under consideration, but rather as a tool to acquire a comparative sense of the toxic risk involved under different conditions and circumstances, thus identifying cases deserving further thorough assessments and possibly the commitment of additional resources. Let us now begin with the presentation of two quite popular modeling frameworks for spill incidents involving volatile liquid hydrocarbons and aqueous solutions in enclosed areas whose main structural features are delineated in (Lee, 2002) and (Guo et al., 2008) respectively. The first modeling framework is structurally simpler and based on a steady/constant evaporation rate for volatile liquid hydrocarbons in a spill incident. It introduces a first-order linear dynamic process model mathematically represented by a single mass balance equation applied to the enclosure volume V under the assumption of ideal mixing (Lee, 2002):
V
dC ¼ E QC dt
(1)
where C is the hydrocarbon vapor concentration, E the evaporation rate and Q the ventilation flow rate (which is of course adjustable). In this simple model the evaporation rate E is considered constant and given by the following expression (Lee, 2002):
E ¼
Mw KAP 0 RT
(2)
where Mw is the molecular weight of the hydrocarbon, A the spill area (constant), P0 the vapor pressure of the hydrocarbon, R the universal gas constant, T the liquid temperature and K the mass transfer coefficient usually calculated through the appropriate empirical expression (Lee, 2002). From equations (1) and (2) one obtains the steady-state vapor concentration:
Cs ¼
E Mw KAP 0 ¼ Q RTQ
(3)
which is used as a measure of exposure concentration (also used in a risk quotients (van Leeuwen & Hermens, 1995; Scheringer et al., 2001) in the risk assessment methodology presented in (Lee, 2002) (using ppm units, expression (3) attains the form: Cs ½ppm ¼ KAP 0 =QP 106 , where P is the partial pressure of the hydrocarbon in air). Furthermore, one can easily integrate the differential equation (1) and obtain the dynamic vapor concentration profile C(t) recognizing that C(t ¼ 0) ¼ 0:
CðtÞ ¼
E Q 1 exp t Q V
(4)
Notice that the quantity s ¼ V=Q is the process time-constant, and as intuitively expected, is inversely proportional to the ventilation flow rate Q and proportional to the enclosure volume V. Quite frequently, in an exposure scenario, the notion of a time-average concentration value C is used (such as the 8-h average one for workers (Scheringer et al., 2001)) as a measure of exposure concentration instead of the steady-state value Cs, and defined as follows (Scheringer et al., 2001):
1 C ¼ T
721
ZT CðtÞdt
(5)
0
where T is a measure of the exposure time or interval. It should be pointed out that C captures the full dynamic history of the vapor concentration profile, whereas Cs is based solely on its asymptotic steady-state characteristics. Given expression (4), the integral in (5) can be analytically calculated leading to:
C ¼
E V Q 1þ exp T 1 Q QT V
(6)
Please notice that when the exposure time T is considerably larger than the process time-constant: T >> s ¼ V=Q , then the above equation (6) yields:
C
T
s
/N
¼
( ) ðexpðTs 1 E E T 1 þ lim ¼ Cs ¼ Q Q ðTs Þ/N s
(7)
and therefore the two measures of exposure concentration would lead to similar risk estimates. However, if T < < 4s, i.e. the exposure time is much shorter than the time practically required to reach steady state in the above spill model, one obtains due to the monotonicity of the function f ðxÞ ¼ expðxÞ 1=x:
exp Ts 1 T s ( ) ðexpðTs 1 E T 1þ C ¼ Q s C Cs
<
ðexpð4Þ 1Þ 0 4
E < 0:8 0 Q
(8)
< 0:8
Therefore, within the above modeling framework and under the above conditions, the use of the steady-state value Cs (as in (Lee, 2002)) instead of the time-average concentration C in a risk assessment framework would unnecessarily overestimate the associated risk, since the dynamic (transient) features of the vapor concentration profile (which obviously become more important in cases with short exposure times) would be overlooked. The main ideas guiding the development of a more sophisticated, comprehensive and experimentally validated model for spill incidents involving aqueous solutions in an indoor environment that allows the more realistic integration of time-varying evaporation rates (particularly monotonically decreasing evaporation rates due to the decreasing concentration profile of the solute in the spilled liquid (Guo, 2002; Guo et al., 2008)) into its structure have been introduced in the excellent work (Guo et al., 2008). The proposed model is a fourth-order linear dynamic process model comprised of four mass balance equations for the mass of the aqueous solution spilled W, the water vapor concentration in the air m, the solute concentration in the spilled liquid CL and the solute concentration in the air C (Guo et al., 2008):
dW dt dm V dt dC VL L dt dC V dt
¼ Rw Rs ¼ Rw þ Q ðmout mÞ ¼ Rs ¼ Rs QC
ð9Þ
where V is the volume of the enclosed area, VL the volume of the aqueous solution remaining on the floor, Rw ¼ Akgw(msat m) is the rate of water evaporation for the spilled liquid with A being the spill area (time-varying), kgw the gas-phase mass transfer coefficient for the solute, msat the saturated water vapor concentration in indoor air, Rs ¼ AKOL ðCL C=HÞ is the rate of solute emission from the
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spilled liquid (obviously time-varying) with KOL being the overall liquid-phase mass transfer coefficient, H Henry’s constant, and finally mout the water vapor concentration in ambient air and Q the air change flow rate. The set of initial conditions that accompanies the above set of dynamic model equations is: (W(t ¼ 0), m(t ¼ 0), CL (t ¼ 0), C(t ¼ 0)) ¼ (W0, mout, CL0, 0), where W0 is the mass of aqueous solution spilled and CL0 the initial solute concentration in the spilled liquid. Under the assumptions that (Guo et al., 2008): i) the water evaporation rate is considerably larger than that of the solute, ii) the moisture content of the indoor environment, i.e. m is approximately constant (supported by experimental evidence (Guo et al., 2008)), iii) the concentration of the solute in indoor air is much lower than its equilibrium concentration (CL > > C/H), the above dynamic equations can be analytically integrated leading to the following time-varying dynamic concentration profile of the solute in the air (Guo et al., 2008):
CðtÞ ¼
A0 KOL CL0 ðexpð NtÞ expð qtÞÞ Vðq NÞ
(10)
where N ¼ Q/V is the air change rate, and q ¼ ðA0 kgw msat ð1 rÞ=W0 Þ þ ðKOL =qÞ, with q ¼ VL/A being the liquid film thickness (considered constant; for a justification please see (Guo et al., 2008)), A0 being the initial spill area and r the relative humidity in indoor air (m/msat). Within the above modeling framework, please notice that the evaporation rate is a monotonically decreasing quantity (Guo et al., 2008):
K t Rs ¼ AKOL CL0 exp OL
q
(11)
and consequently, the concentration C(t) asymptotically approaches the zero value in agreement with the intuitively expected behavior under realistic conditions. Furthermore, one can show that the above concentration profile attains a maximum value given by the following expression:
Cmax
A K C ¼ 0 OL L0 Vðq NÞ
( N q ) N qN N qN q q
K ¼ CT
(14)
where C is the exposure concentration, T the exposure time and K a constant related to a specific level of fatalities in a population. Haber’s law suggests that fatal health responses by members of a population remain essentially invariant for various exposure scenarios as long as the product CT stays constant: reducing the exposure time by half while doubling the exposure concentration value would lead to the same level of toxicity risk and similar health responses. Quite often the product CT is known as the toxic load and denoted by: L ¼ CT (this symbol will be retained throughout the present paper to denote toxic load), or the “infinitesimal” dL ¼ C(t) dt (toxic load in differential form) whenever the concentration profile is time-varying. Indeed, Haber’s law was also used in cases where concentration profiles were not necessarily constant, with C in the original form (14) being now replaced by the time-average concentration C (Hilderman et al., 1999). The rationale behind such a use, is that the total toxic load under Haber’s law in the case of time-varying concentrations (and hence the associated health effects) remains invariant:
Z L ¼
0
T
Z dL ¼
0
T
CðtÞdt ¼ CT
(15)
However, new experimental studies, toxicological observations and empirical findings elucidated the inherent limitations of Haber’s law (ten Berge et al., 1986; Hilderman et al., 1999; Ride, 1984):
(12)
For this particular spill model, a time-average exposure concentration value C can be analytically computed as well:
Z 1 T CðtÞdt T 0 A K C 1 1 ¼ 0 OL L0 ½expðqTÞ 1 ½expðNTÞ 1 Vðq NÞT q N
to exposure to toxic chemicals have early moorings in the tumultuous scientific career and tragic personal life of Fritz Haber who was the architect of the development of the chemical weapons program of the German army in early 20th century. On the basis of preliminary evidence accumulated through the use of poison gases for military purposes, Haber postulated that fatal toxicity can be described through the following simple law (Andersen, 2003; ten Berge et al., 1986; Hilderman et al., 1999; Holland & Sielken, 1993; Ride, 1984):
C ¼
(13)
which can be considered as a measure of exposure concentration in risk assessment studies. 3. The proposed toxicity risk assessment method Traditionally, toxicological experiments have been conducted in such a way that laboratory animals are exposed to constant concentration levels of the toxic chemical under consideration for a fixed period of time and the corresponding number of fatalities is observed and recorded (Andersen, 2003; Holland & Sielken, 1993; van Leeuwen & Hermens, 1995). From a practical point of view, the selection of the number of fatalities as a health end-point in toxicological studies of this nature is justified since less severe effects on health, even if observed, can not be easily quantified and are inherently associated with significant variability within a certain population (Andersen, 2003; Hilderman et al., 1999; Holland & Sielken, 1993; van Leeuwen & Hermens, 1995). Historically, acute toxicity studies and mortality rates due
i) Regardless of how low the exposure concentration levels are, fatalities should be observed as long as the exposure time becomes quite large. This prediction of Haber’s law leads to overestimating the health effects at low concentration levels, a prediction empirically refuted and theoretically weak since it overlooks the underlying physiological mechanisms associated with recovery processes. ii) The health effects due to high exposure concentration levels can be modulated by shortening the exposure time. This prediction of Haber’s law leads to underestimating the severity of health effects often observed in acute toxicity episodes due to the underlying complexity of the physiological mechanisms activated in order to cope with an “overwhelming” short exposure to high toxic concentration levels. In light of i) and ii), toxicologists introduced nonlinear generalizations of Haber’s law which attain the following form (ten Berge et al., 1986; Hilderman et al., 1999; Ride, 1984):
L ¼ CnT
(16)
where the exponent n is associated with the particular chemical and customarily determined through experiments (with typical values n 1). Notice that the above nonlinear generalization of Haber’s toxic load is in agreement with the empirical evidence in cases i) and ii), i.e. the behavior of toxic load realistically expected under low and high exposure concentration levels. As before, in the case of time-varying concentration profiles one could use the
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time-average exposure concentration value C in the above nonlinear generalization: n
Lm ¼ C T
(17)
and thus introduce the notion of a “mean” toxic load for the exposure duration. Notice however that in the nonlinear case n > 1 (as opposed to the linear one where n ¼ 1) the dynamic changes in C ¼ C(t) do matter, and the overall or total toxic load which is properly defined as follows:
Z Lt ¼
T
0
Z dL ¼
T
0
C n ðtÞdt
(18)
( Qn ðC1 ; .; Cm Þ ¼
m 1X Cn m i¼1 i
Z Lt ¼
T
0
Z dL ¼
0
T
n
C n ðtÞdt C T ¼ Lm
(19)
thus representing a quite useful upper bound on toxic loads when evaluating toxicity risk and associated health effects such as fatalities. At this point, a mathematical justification is provided of the above result. Consider the standard Riemann representation of the integral in (18):
Lt ¼ lim
m/N
m X i¼1
Cin ðDtÞ
(20)
under a partition of the exposure interval with mesh: ðDtÞ ¼ T=m and Ci ¼ C(ti) with ti ˛½ðT=mÞi; T=mði þ 1Þ. Similarly, under the same Riemann partition, one obtains: n
Lm ¼ C T ¼
1 T n1
(Z
)n
T
CðtÞdt 0
¼
1 T n1
( lim
m/N
m X
)n Ci ðDtÞ
i¼1
(21) Define now the quantity:
)1 n
(22)
with C1, ., Cm > 0. Notice that:
Q1 ðC1 ; .; Cm Þ ¼
m 1X C m i¼1 i
(23)
Using the generalized mean inequality for n > 1 (Hardy, Littlewood, & Pólya, 1988), the following inequality can be established:
)1 ( n m m P P 1 1 Qn ðC1 ; .; Cm ÞiQ1 ðC1 ; .; Cm Þ0 m Cin > m Ci 0 i¼1 i¼1 ( )n ( )n m m m m X X 1X 1 X ðDtÞn Cin > n Ci 0ðDtÞ Cin > C 0 i m i¼1 m ðmDtÞn1 i ¼ 1 i ¼)1 i¼1 ( ( )n n m m m X X X Pm 1 1 n n Ci ðDtÞ 0 lim Ci ðDtÞ n1 lim Ci ðDtÞ 0Lt Lm i ¼ 1 Ci ðDtÞ > n1 m/N m/N T T i¼1 i¼1 i¼1
is not equal to (17) any more: Lt s Lm. In the special case of a constant concentration profile where C ¼ C(t) ¼ M ¼ constant, then, even in the nonlinear case (n > 1), C ¼ M and Lt ¼ MnT ¼ Lm. The reader is reminded that in a typical toxicological experiment the exposure concentration profile C is constant by design, and therefore, no particular concern is caused about the choice and use of the proper toxic load model. In a spill incident however, the exposure concentration C is realistically expected to vary with time (within the exposure time-window), and the selection of total toxic load (18) is regarded as more useful since it captures the simultaneous effect of nonlinear and time-varying exposure concentrations on toxicity (ten Berge et al., 1986; Hilderman et al., 1999; Ride, 1984). From a risk assessment, as well as regulatory perspective, it is also important to show that in the nonlinear case where n > 1, the total toxic load Lt is larger than the mean toxic load Lm:
723
(24)
Motivated by the ideas introduced in (Hilderman et al., 1999), one should acknowledge that the notion of overall/total toxic load (18), despite its advantages, still lacks a degree of realism when used for the assessment of toxicity risks in a real exposure scenario following a spill incident such the ones under consideration. Indeed, the recognition that it does not capture the undeniable facts that: A) the uptake of any exposure concentration can not be instantaneous but rather one needs to consider an effective exposure concentration or dose available at the receptor site which potentially influences health effects estimates (the number of fatalities in our case), and B) the underlying biological recovery processes do contribute to the health response of a population to toxic exposure, and that toxic loads can not increase indefinitely as time progresses and effective concentration levels become quite low. Apparently, a scientifically thorough and detailed description of cases A) and B) would require the development of a comprehensive and quite often complex physiologically based pharmacokinetic model that by itself could pose considerable challenges (considering all possible exposure routes, metabolic pathways, the fate of the chemical inside the body, etc. which inevitably introduce a large number of parameters that need to be reliably estimated) (Andersen, 2003; Hilderman et al., 1999; Holland & Sielken, 1993; Ramaswami et al., 2005). Instead, as the authors show in (Hilderman et al., 1999), a simple first-order dynamic description of an effective exposure concentration Ceff available at the receptor site could be introduced, and its relationship to the concentration C of the toxic vapor (obtained from a spill model) represented by:
dCeff 1 C Ceff ¼ sup dt
(25)
where sup is an empirical parameter called the uptake timeconstant. Notice that small uptake time-constants sup /0 lead almost instantaneously to: Ceff /C, whereas very large ones
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sup /N to Ceff /0 as intuitively expected. For any finite value 0 < sup < N, one also concludes that asymptotically
limt/N Ceff ¼ C. In this case it is of course presupposed that the exposure period T is quite large: T > > 4sup, otherwise, if T < 4sup, then Ceff has not yet converged to C. This behavior is certainly expected, since the above simple dynamic model nicely captures the fact that the uptake process is not instantaneous and the short exposure duration does not allow enough time for the effective concentration level Ceff at the receptor site to reach C the concentration of the toxic vapor. Finally, it should be pointed out that a more detailed uptake model based on “first-principles” would have to integrate all possible exposure and absorption routes (inhalation path involving nose, throat and lungs in which case Ceff is the concentration in the airways, metabolic paths involving the bloodstream, absorption and transfer mechanisms between the lungs and blood in which case Ceff is the concentration in the bloodstream, etc.) (Andersen, 2003; Hilderman et al., 1999; Holland & Sielken, 1993). On the basis of the notion of effective exposure concentration Ceff, the notion of overall/total toxic load can be modified as follows:
Z Leff ¼
T 0
Z dL ¼
T 0
n Ceff ðtÞdt
(26)
by introducing an effective toxic load Leff through which the assumption of instantaneous uptake is relaxed. With respect to case B), one should also be cognizant of the role of complex underlying biological mechanisms (metabolic degradation of the chemical’s toxicity, excretion mechanisms, physiological repair of damaged tissue) responsible for recovery processes as evidenced by numerous studies (Andersen, 2003; Hilderman et al., 1999; Ramaswami et al., 2005). These of course tend to naturally reduce the effective toxic load. In such a case, a simple first-order recovery model for the effective toxic load can be proposed (Hilderman et al., 1999):
dLeff 1 n Leff ¼ Ceff sr dt
(27)
where sr is the recovery time-constant. Notice that (27) further generalizes the effective toxic load model of (26):
dLeff n ¼ Ceff dt
(28)
by capturing also the effect of recovery processes. When sr /N (no recovery), the two models for Leff coincide. If sr /0 (immediate recovery), then Leff /0 as expected. In cases where 0 < sr < N, equation (27) describes the expected gradual decline of the effective toxic load values due to the latent recovery processes. Summarizing, in the case of a noninstantaneous uptake the following toxic load model is proposed:
dCeff 1 C Ceff ¼ sup dt dLeff n ¼ Ceff dt
(29)
with Ceff(t ¼ 0) ¼ 0, Leff(t ¼ 0) ¼ 0 and C(t) representing the toxic vapor concentration profile as given by the spill model equations presented in Section 2. In cases where recovery processes are taken explicitly into account, the proposed toxic load model takes the following form:
dCeff 1 C Ceff ¼ sup dt dLeff 1 n Leff ¼ Ceff sr dt
(30)
with Ceff(t ¼ 0) ¼ 0, Leff(t ¼ 0) ¼ 0 and C(t) representing the toxic vapor concentration profile obtained through the spill model equations presented in Section 2. Given the availability of a working spill model and a model for the effective toxic load, the last remaining component of a quantitative toxicity risk assessment framework is the development of a risk model (a type of doseeresponse relationship) that relates the effective toxic load to the number of fatalities (or a percentage) in a population due to exposure to a toxic vapor resulting from a spill incident. At this point, the reader is reminded of the two dimensions of a quantitative chemical risk assessment methodological framework: the “size of risk” as realized through the notion of risk quotient (the ratio of Ceff to a threshold value such as PEL or IDLH), and the “consequences of risk” as realized through the appropriate doseeresponse relationship and a specific health end-point (fatalities for example in toxicity studies). In the context of the present study, a probit doseeresponse model is proposed (Finney, 1971; Hilderman et al., 1999; Holland & Sielken, 1993). According to this methodology the variability of individual tolerances to toxic chemicals is recognized (Holland & Sielken, 1993). In particular, it is assumed that a certain threshold dose or toxic load Leffth exists for each individual, but such a threshold toxic load value varies amongst the members of a population. Furthermore, it is assumed that the individual threshold toxic load Leffth is log normally distributed with a certain logarithmic mean m and standard deviation s (an assumption owing its justification to experimental findings and empirical data (Hilderman et al., 1999; Holland & Sielken, 1993)). Therefore, the expected percentage of fatalities P due to exposure to a certain toxic load Leff would be determined by a threshold load that satisfies the inequality: Leffth < Leff, and thus given by the cumulative distribution function shown below:
1 P ¼ pffiffiffiffiffiffiffi 2ps
Z
(
lnLeff
N
exp
) 1 xm 2 dx s 2
(31)
The above expression (31) can be rewritten through a standard change of variables as follows (Finney,1971; Holland & Sielken,1993):
Z aþblnLeff
1 1 P ¼ pffiffiffiffiffiffiffi exp y2 dy ¼ F a þ b ln Leff 2 2p N
(32)
where F is the standard normal integral (Finney, 1971). One now defines the probit variable Pr:
Prha þ bln Leff
(33)
and therefore:
P ¼ FðPrÞ
(34)
Notice that a, b coefficients in the above change of variables in integral (32) are related to (m, s) of the above health response distribution, depend on the specific chemical and are determined in practice through experiments and on the basis of empirical data. For a specific value of the effective toxic load Leff, equation (33) gives the associated value of the probit variable Pr, and finally the percentage of fatalities is obtained by using equation (34) (specifically, tabulated values of the standard normal integral corresponding to various values of its argument). Conversely, for a certain percentage of fatalities, one inverts the P ¼ F(Pr) relationship computing the associated value of the probit variable Pr, and then, using equation (33) the corresponding value of the effective toxic load Leff that induces the aforementioned percentage of fatalities is estimated. In the next Section, the proposed toxicity risk assessment method is evaluated through simulation studies in a case study involving a spill episode of ammonia solution in an enclosed area.
N. Kazantzis, V. Kazantzi / Journal of Loss Prevention in the Process Industries 23 (2010) 719e726
4. Illustrative example: toxicity risk assessment for an ammonia spill incident
Table 2 Spill incident II e process parameter values.
Pr ¼ a þ b ln Leff
(35)
with a ¼ 15.8, b ¼ 1, n ¼ 2, since it appears to be in closer agreement with experimental results and methodologically consistent with toxicological requirements involving more realistic health responses of humans to toxic vapors (Schubach, 1995). The 1% fatalities level corresponding to a probit variable value of: Pr z 2.6 is considered that is often related to a toxic load or concentration threshold value close to the Immediately Dangerous to Life and Health Limit (IDLH). Indeed, using equation (33), one can explicitly calculate the corresponding level of effective toxic load: 7 2 3 L[1] eff ¼ 9.7 10 [(mg) (min)/m )] that is probabilistically expected to induce 1% fatalities. In the first case, an acute exposure scenario is considered where immediately after the spill and for a relatively short period of time, the exposure concentration fluctuates drastically attaining a maximum value of: Cmax z 5980 [mg/m3] which is perilously close to levels characterized as severe by various regulatory agencies (Schubach, 1995; U.S. Department of Health and Human Services, 2004), rapidly decreasing afterwards to much lower levels so that the 8-h average concentration value Cz35 [mg/m3] stays close to the “safe” PEL level. In Fig. 1, please notice that the total toxic load model (18) (in this case we consider the simpler model with instantaneous uptake and no recovery denoted by L1) crosses the L[1] eff level that induces 1% fatalities after
Table 1 Spill Incident I e Process parameter values. Process parameters
Values
kgw KOL msat r A0 W0 V N ¼ Q/V
12.5 mh1 4E-3 mh1 18 g3 0.69 20.7 m2 15.4 kg 30 m3 0.4 min1 9.6E-6 m 1E6 g3
q
Process parameters
Values
kgw KOL msat r A0 W0 V N ¼ Q/V
12.5 mh1 4E-3 mh1 18 g3 0.69 0.207 m2 154.3 g 30 m3 0.004 min1 9.6E-4 m 1E4 g3
q
CLO
approximately 5 min, capturing nicely the severity of the underlying acute exposure scenario. This behavior is contrasted with a toxic load model based on the 8-h average (mean) concentration value Cz35 [mg/m3], which, as shown in Fig. 1, grossly underestimates the associated toxicity risk. Therefore, this particular case illustrates that it is certainly more advantageous to use even the simple total toxic load model (18) in spill incidents, when compared to more traditional models that use time-average (mean) or other constant exposure concentration values. In the second case, a different spill incident is considered under conditions close to the experimental ones reported in (Guo et al., 2008). In this case, the exposure concentration fluctuates mildly within a larger exposure window reaching a maximum value of Cmax z 60 [mg/m3]. This is certainly a case of negligible toxicity risk since all concentration values remain close to the PEL value, and the standard regulatory characterization of ammonia toxicity under these conditions is practically risk-free. The proposed effective toxic load model (30) was used in our simulation studies with an uptake time-constant sup ¼ 1[s] (a reasonable value under the assumption that the uptake rate is determined by the inhalation rate in similar cases as justified in (Hilderman et al., 1999; U.S. Department of Health and Human Services, 2004)) and a recovery time-constant sr ¼ 20[min] (a reasonable value justified in light of empirical findings and results from experimental studies on underlying physiological, metabolic toxicity reduction and excretion mechanisms involving ammonia as discussed in (U.S. Department of Health and Human Services, 2004)). Based on the simulation results graphically depicted in Fig. 2, notice that the proposed
8
10
6
10 Load (mg/m3)2 min
An aqueous ammonia solution conforming to the specifications of the one used in the experimental study (Guo et al., 2008) is considered (1.3% (w/w) concentration) and spill episodes are simulated with the aid of the second model presented in Section 2. In all the ensuing simulation runs all mass transfer coefficient values as well as inherent physicochemical properties of the ammonia solution are the same as the ones considered in the experimental investigations in (Guo et al., 2008) that were conducted in order to validate the associated spill model. The rest of the model input variables such as the enclosure volume, ventilation rate, initial concentration of the aqueous solution, amount of solution spilled, initial spill area could vary giving rise to different scenarios. For the particular cases or spill incidents considered in the present study the above sets of model input values are tabulated and presented in Tables 1 and 2. It should be also pointed out that in both the above scenarios which physically correspond to drastically different spill episodes, the same 8-h average (mean) concentration value Cz35 [mg/m3] is considered, a value close to the Permissible Exposure Limit (PEL) value as set by OSHA (U.S. Department of Health and Human Services, 2004). Furthermore, the probit doseeresponse model equation used for the ammonia solution was the one developed by the Netherlands Organization of Applied Scientific Research (TNO):
CLO
725
4
10
2
10
L1 (instantaneous) L(1% fatalities) Load (mean)
0
10
−2
10
−1
10
0
10
1
10
t[min] Fig. 1. Spill incident I: Toxic load versus time curves.
2
10
726
N. Kazantzis, V. Kazantzi / Journal of Loss Prevention in the Process Industries 23 (2010) 719e726
provides the requisite degree of differentiation between the exposure concentration obtained through the aforementioned models and the effective concentration that reaches the receptor site as determined by a finite uptake rate of the toxic vapor/gas. Furthermore, on the basis of the time-varying effective concentration, an effective toxic load that takes into account latent recovery processes was integrated into a probit methodological framework within which the quantification of a population response to toxic exposure was made possible. Finally, the proposed method was evaluated in a case study involving a spill episode of ammonia solution in an enclosed area.
5
5
x 10
L1(effective) L2(instantaneous) L3(mean)
4.5 4
Load (mg/m3)2 min
3.5 3 2.5 2 1.5
Acknowledgements
1 0.5 0
0
50
100
150
200
250
300
350
t[min] Fig. 2. Spill incident II: Toxic load versus time curves.
The authors would like to thank Professor S. M. Mannan and his Associates at the Mary Kay O’Connor Process Safety Center, Department of Chemical Engineering, Texas A&M University for their kind invitation to participate in the 2009 International Process Safety Symposium. They are also indebted to the anonymous reviewers for their thoughtful suggestions and helpful remarks. References
effective toxic load (denoted by L1) has the capacity to realistically capture the very low risk level under the set of conditions associated with the particular spill incident considered in this case. However, in such a case, both the toxic load with instantaneous uptake and no recovery (denoted by L2), as well as the toxic load based on the 8-h average (mean) concentration value Cz35 [mg/m3] predict unreasonably high risk levels, i.e. after a certain exposure period they both cross the L[1] eff level of 1% fatalities, thus contradicting the established safety threshold values and limits (such as PELs) which are deliberately set by regulatory authorities in a conservative precautionary manner, and certainly orders of magnitude below any fatalities-producing exposure concentration levels. Therefore, as shown in this second case, the proposed quantitative toxicity risk assessment method appears to carry considerable merit when comparatively evaluated against more traditional ones in pertinent studies. 5. Concluding remarks A new method for the assessment of toxicity risk due to spill episodes involving volatile liquid hydrocarbons and aqueous solutions in enclosed areas was proposed. Source models with timevarying evaporation and emission rates were used in conjunction with appropriate mass transfer models to estimate dynamic concentration profiles of potentially toxic pollutants following spills of volatile liquid hydrocarbons as well as aqueous solutions in an indoor environment. Relaxing the assumption found in more traditional approaches to toxicity risk assessment where toxic loads are estimated under constant concentration levels of the toxic pollutant, it was shown that the proposed approach takes explicitly into account the dynamic features of the concentration profile during the time of exposure. Furthermore, the proposed method incorporated the idea of using a simple dynamic description that
Andersen, M. E. (2003). Toxicokinetic modeling and its applications in chemical risk assessment. Toxicology Letters, 138, 9e27. ten Berge, W. F., Zwart, A., & Appelman, L. M. (1986). Concentration-time mortality response relationship of irritant and systematically acting vapours and gases. Journal of Hazardous Materials, 13, 301e309. Finney, D. J. (1971). Probit analysis. Cambridge, UK: Cambridge University Press. Guo, Z. (2002). Review of indoor emission source models. Part 1. Overview. Environmental Pollution, 120, 533e549. Guo, Z., Sparks, L. E., & Roache, N. F. (2008). Modeling small-scale spills of aqueous solutions in the indoor environment. Journal of Hazardous Materials, 153, 444e453. Hardy, G. H., Littlewood, J. E., & Pólya, G. (1988). Inequalities. Cambridge, UK: Cambridge University Press. Hilderman, T. L., Hrudey, S. E., & Wilson, D. J. (1999). A model for effective toxic load from fluctuating gas concentrations. Journal of Hazardous Material, 64, 115e134. Holland, C. D., & Sielken, R. L. (1993). Quantitative cancer modeling and risk assessment. New York: Prentice Hall. Lee, K. W. (2002). A methodology for assessing risk from released hydrocarbon in an enclosed area. Journal of Loss Prevention in the Process Industries, 15, 11e17. van Leeuwen, C. J., & Hermens, J. L. M. (1995). Risk assessment of chemicals: An introduction. Dordrecht, The Netherlands: Kluwer. Louvar, J. F., & Louvar, B. D. (1997). Health and environmental risk analysis. New York: Prentice Hall. Ramaswami, A., Milford, J. B., & Small, M. J. (2005). Integrated environmental modeling. Hoboken, NJ: Wiley. Ride, D. J. (1984). An assessment of the effects of fluctuations on the severity of poisoning by toxic vapours. Journal of Hazardous Materials, 9, 235e240. Scheringer, M. (2002). Persistence and spatial range of environmental chemicals: New ethical and scientific concepts for risk assessment. Darmstadt, Germany: Wiley. Scheringer, M., Vögl, T., von Grote, J., Capaul, B., Schubert, R., & Hungerbühler, K. (2001). Scenario-based risk assessment of multi-use chemicals: application to solvents. Risk Analysis, 21, 481e497. Schubach, S. (1995). Comparison of probit expressions for the prediction of lethality due to toxic exposure. Journal of Loss Prevention in the Process Industries, 8, 197e204. Slovic, P., Finucane, M. L., Peters, E., & MacGregor, D. G. (2004). Risk as analysis and risk as feelings: some thoughts about affect, reason, risk and rationality. Risk Analysis, 24, 311e322. Trapp, S., & Matthies, M. (1998). Chemodynamics and environmental modeling: An introduction. Heidelberg, Germany: Springer. U.S. Department of Health and Human Services. (2004). Toxicological profile of ammonia. Washington D.C.: Agency for Toxic Substances and Disease Registry.
Contents lists available at ScienceDirect
Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
A toxicity risk assessment method for spill incidents involving volatile liquid hydrocarbons and aqueous solutions in enclosed areas Nikolaos Kazantzis a, *, Vasiliki Kazantzi b a b
Department of Chemical Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609-2280, USA Department of Project Management, Technological Educational Institute (TEI) of Larissa, Larissa 41110, Greece
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 February 2010 Received in revised form 19 May 2010 Accepted 4 June 2010
A new method for the assessment of toxicity risk due to spill incidents involving volatile liquid hydrocarbons and aqueous solutions in enclosed areas is proposed. First, mass transfer models coupled with time-varying evaporation and emission rates (source models) are used to estimate the dynamic concentration profiles of potentially toxic gas/vapor pollutants resulting from spills of volatile liquid hydrocarbons as well as aqueous solutions in an enclosed area or indoor environment. Recognizing that toxicity risk depends nonlinearly on exposure duration and concentration, while the latter varies dynamically with time at any receptor position, the use of the aforementioned models to reliably compute toxic loads in the presence of time-varying concentration profiles is pursued explicitly in the present study. In this manner, one effectively overcomes the limitations of more traditional approaches to toxicity risk assessment where toxic loads are estimated under constant (steady state, average or mean) concentration levels of the toxic pollutant. Furthermore, instead of resorting to complex physiologically inspired pharmacokinetic models and the associated formidable multi-parameter estimation problems requiring the availability of large sets of good and reliable data, the proposed method incorporates also the idea of using a simple dynamic description that provides the requisite degree of differentiation between the exposure concentration obtained through the above models and the effective concentration (often associated with dose) that reaches the receptor site as determined by the uptake rate of a toxic vapor/gas. On the basis of the timevarying effective concentration or dose, an effective toxic load that takes into account potential recovery processes is then computed and integrated into a probit methodological framework where the proper quantification of a population response to toxic exposure (effective toxic load) provides the means to assess and characterize toxicity risk. Finally, the proposed method is evaluated through simulation studies in a case study involving a spill episode of ammonia solution in an enclosed area. 2010 Elsevier Ltd. All rights reserved.
Keywords: Chemical risk assessment Spill incidents Volatile liquid hydrocarbons Aqueous solutions Time-varying emission rates Toxicity assessment
1. Introduction The quantification of risk assessment associated with incidents involving the natural, accidental or intentional release of potentially hazardous chemicals into the environment has been recognized as a rather useful methodological paradigm and well-justified research endeavor by the scientific community, provided that its inherent limitations and extent of scope are carefully acknowledged in a complex world where uncertainty reigns (Holland & Sielken, 1993; van Leeuwen & Hermens, 1995; Louvar & Louvar, 1997; Ramaswami, Milford, & Small, 2005; Scheringer, 2002; Trapp & Matthies, 1998). In the presence of complexity, quantitative risk models with varying degrees of sophistication should aim at * Corresponding author. Tel.: þ1 508 8315666; fax: þ1 508 8315853. E-mail addresses: [email protected] (N. Kazantzis), [email protected] (V. Kazantzi). 0950-4230/$ e see front matter 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jlp.2010.06.005
complementing and skillfully guiding intuition, which should be also exercised as models aspire to capture even value-laden facets of complex situations (Holland & Sielken, 1993; van Leeuwen & Hermens, 1995; Louvar & Louvar, 1997; Scheringer et al., 2001; Slovic, Finucane, Peters, & MacGregor, 2004). Given: 1) the considerable uncertainties in modeling emission/release conditions, 2) the complexity of the combined effect of inherent physicochemical properties and environmental processes on the fate of a chemical, 3) the physiological responses of individuals to different levels of exposure (notwithstanding the variability within a certain population), and 4) the paucity of reliable data at all the above stages, risk models should not be expected to provide the “right answer” and generate predictions endowed with absolute mathematical precision, but
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instead become useful tools enabling scientists to ask the right questions without resorting to costly experimentation (Holland & Sielken, 1993; Louvar & Louvar, 1997; Ramaswami et al., 2005; Scheringer, 2002; Scheringer et al., 2001; Slovic et al., 2004; van Leeuwen & Hermens, 1995). Indeed, they could be used to: i) identify the sources of uncertainty with the highest impact on risk assessment, and/or ii) identify conditions under which significant risk might occur, and/or iii) form the basis of a reliable risk-informed screening method Therefore, the above quantitative risk assessment methods should allow for (the finite) available resources to be concentrated on and emphasis to be placed on cases where furthermore detailed assessment is needed in order to reduce uncertainty and mitigate/ manage risk (van Leeuwen & Hermens, 1995; Scheringer, 2002; Scheringer et al., 2001). Under this spirit, the present study aims at developing a quantitative framework for the assessment of toxicity risk posed by spill incidents involving volatile liquid hydrocarbons and aqueous solutions in an enclosed area or indoor environment. Following the principles of the conceptual framework presented in (van Leeuwen & Hermens, 1995; Scheringer et al., 2001), one is first reminded that hazard identification is related to the inherent physicochemical properties of the chemical under consideration as well as the occurrence conditions of the spill incident itself. Furthermore, the overall risk is quantitatively represented as the product of the probability of occurrence of the above incident multiplied by the conditional probability of observing a fatality (the health end-point in the present study) due to exposure to toxic vapor given the occurrence of the spill incident. Notice that the second probabilistic term in the overall risk is the term traditionally associated with chemical risk assessment which also captures the effects (or consequences) on public health and/or ecosystem functions (van Leeuwen & Hermens, 1995; Scheringer, 2002; Scheringer et al., 2001). Chemical risk depends explicitly on a measure of exposure or dose which can be in principle estimated through a chemodynamics model that explicitly takes into account the combined effect of inherent physicochemical properties and underlying environmental processes on the fate of the chemical, often in conjunction with a physiologically inspired pharmacokinetic model in order to determine the physiologically important effective dose (Andersen, 2003; Holland & Sielken, 1993; van Leeuwen & Hermens, 1995; Ramaswami et al., 2005; Scheringer, 2002; Trapp & Matthies, 1998). Typically, a quantitative sense of the size or significance of risk is obtained through the notion of risk quotient which is based on a direct comparison of the aforementioned exposure measure or dose to an effect level or threshold concentration such as the Permissible Exposure Limit (PEL) or the Immediately Dangerous to Life and Health Limit (IDLH) (van Leeuwen & Hermens, 1995; Louvar & Louvar, 1997; Ramaswami et al., 2005; Scheringer, 2002; Scheringer et al., 2001). Finally, the extent or consequences of the above risk are quantified through a doseresponse type of relationship such as the one associated with a probit model, which, within the context of the present study, could provide a probabilistic measure of an expected number (or percentage) of fatalities due to exposure to toxic vapor of a certain population (Finney, 1971; Lee, 2002; van Leeuwen & Hermens, 1995; Louvar & Louvar, 1997; Ramaswami et al., 2005; Scheringer et al., 2001). Overcoming some of the limitations associated with existing approaches, the proposed method: i) allows a more realistic time-varying rather than constant evaporation/emission rate to be incorporated into a spill model as in (Guo, 2002; Guo, Sparks, & Roache, 2008) ii) uses explicitly a more realistic description of toxic load resulting from a spill incident as a nonlinear time-varying
dynamic quantity rather than one based on a constant (steady state, average or mean) concentration profile (Lee, 2002), and incorporates it into an appropriate probit model. Indeed, it has been convincingly demonstrated that nonlinear toxic load models generalizing the traditional Haber’s law in toxicology are more suitable to reliably quantify the combined health effect of exposure concentration and exposure time/ duration (ten Berge, Zwart, & Appelman, 1986; Hilderman, Hrudey, & Wilson, 1999; Ride, 1984). In particular, they overcome the limitations of Haber’s law associated with overestimating health responses to low concentrations and large exposure times, as well as underestimating health responses at high concentrations and short exposure times (as in acute toxicity episodes) (Hilderman et al., 1999; Holland & Sielken, 1993; Ride, 1984; ten Berge et al., 1986). Furthermore, the above nonlinear generalizations of Haber’s law profoundly change the effect of time-varying dynamic concentration profiles during the exposure window on health responses compared to constant concentration values (steady state, average or mean) (ten Berge et al., 1986; Hilderman et al., 1999; Ride, 1984), and this should be necessarily taken into account by any reliable chemical risk assessment model for spill incidents. iii motivated by the ideas introduced in the excellent work (Hilderman et al., 1999), bypasses the complexity and challenges that often accompany the development of a comprehensive physiologically based pharmacokinetic model to quantify the physiologically relevant effective concentration or dose available at the receptor site (Andersen, 2003; Holland & Sielken, 1993; Ramaswami et al., 2005). This is achieved by introducing: 1) a simple linear first-order dynamic description with an empirical parameter called the uptake time-constant relating the toxic vapor concentration in the enclosed area calculated through the spill model to the effective concentration (dose) responsible for health effects, and 2) a second linear first-order dynamic description with an empirical parameter called the recovery time-constant that captures underlying physiological recovery processes (metabolic reduction of chemical toxicity in the human body, excretion mechanisms, tissue repair mechanisms, etc). On the basis of the above models, an effective toxic load is then defined and integrated into a probit methodological framework (Finney, 1971; Holland & Sielken, 1993) where the proper quantification of a population response to toxic exposure (effective toxic load) provides the means to assess and characterize toxicity risk. The present paper is organized as follows: Section 2 encompasses the requisite preliminaries associated with spill models involving volatile liquid hydrocarbons and aqueous solutions in an indoor environment, as well as the traditional structure of a probit model for toxicity risk assessment due to exposure to toxic vapor produced by the above spill incidents. The paper’s main results and proposed method are presented in Section 3, followed by its evaluation in a case study discussed in Section 4 focusing on a spill incident of ammonia solution in an enclosed area. Finally, a few concluding remarks are provided in Section 5. 2. Spill models for volatile liquid hydrocarbons and aqueous solutions in enclosed areas As mentioned in the introductory Section 1, the proposed risk assessment method involving spill incidents of volatile liquid hydrocarbons and aqueous solutions relies on the integrated use of an appropriate spill model coupled with a probit model and
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a model for the effective toxic load that explicitly take into account the dynamic time-varying nature of both the emission/evaporation rate and toxic vapor concentration profiles, a physiologically important effective concentration profile at the appropriate receptor site, as well as the nonlinearity of the health response of a population to a particular exposure pattern. At this point, the reader is reminded that modeling within the context of the proposed quantitative toxicity risk assessment methodology is viewed not as a means to provide a level of absolute accuracy and reality capturing capacity in its predictions for an inherently complex phenomenon such as the one under consideration, but rather as a tool to acquire a comparative sense of the toxic risk involved under different conditions and circumstances, thus identifying cases deserving further thorough assessments and possibly the commitment of additional resources. Let us now begin with the presentation of two quite popular modeling frameworks for spill incidents involving volatile liquid hydrocarbons and aqueous solutions in enclosed areas whose main structural features are delineated in (Lee, 2002) and (Guo et al., 2008) respectively. The first modeling framework is structurally simpler and based on a steady/constant evaporation rate for volatile liquid hydrocarbons in a spill incident. It introduces a first-order linear dynamic process model mathematically represented by a single mass balance equation applied to the enclosure volume V under the assumption of ideal mixing (Lee, 2002):
V
dC ¼ E QC dt
(1)
where C is the hydrocarbon vapor concentration, E the evaporation rate and Q the ventilation flow rate (which is of course adjustable). In this simple model the evaporation rate E is considered constant and given by the following expression (Lee, 2002):
E ¼
Mw KAP 0 RT
(2)
where Mw is the molecular weight of the hydrocarbon, A the spill area (constant), P0 the vapor pressure of the hydrocarbon, R the universal gas constant, T the liquid temperature and K the mass transfer coefficient usually calculated through the appropriate empirical expression (Lee, 2002). From equations (1) and (2) one obtains the steady-state vapor concentration:
Cs ¼
E Mw KAP 0 ¼ Q RTQ
(3)
which is used as a measure of exposure concentration (also used in a risk quotients (van Leeuwen & Hermens, 1995; Scheringer et al., 2001) in the risk assessment methodology presented in (Lee, 2002) (using ppm units, expression (3) attains the form: Cs ½ppm ¼ KAP 0 =QP 106 , where P is the partial pressure of the hydrocarbon in air). Furthermore, one can easily integrate the differential equation (1) and obtain the dynamic vapor concentration profile C(t) recognizing that C(t ¼ 0) ¼ 0:
CðtÞ ¼
E Q 1 exp t Q V
(4)
Notice that the quantity s ¼ V=Q is the process time-constant, and as intuitively expected, is inversely proportional to the ventilation flow rate Q and proportional to the enclosure volume V. Quite frequently, in an exposure scenario, the notion of a time-average concentration value C is used (such as the 8-h average one for workers (Scheringer et al., 2001)) as a measure of exposure concentration instead of the steady-state value Cs, and defined as follows (Scheringer et al., 2001):
1 C ¼ T
721
ZT CðtÞdt
(5)
0
where T is a measure of the exposure time or interval. It should be pointed out that C captures the full dynamic history of the vapor concentration profile, whereas Cs is based solely on its asymptotic steady-state characteristics. Given expression (4), the integral in (5) can be analytically calculated leading to:
C ¼
E V Q 1þ exp T 1 Q QT V
(6)
Please notice that when the exposure time T is considerably larger than the process time-constant: T >> s ¼ V=Q , then the above equation (6) yields:
C
T
s
/N
¼
( ) ðexpðTs 1 E E T 1 þ lim ¼ Cs ¼ Q Q ðTs Þ/N s
(7)
and therefore the two measures of exposure concentration would lead to similar risk estimates. However, if T < < 4s, i.e. the exposure time is much shorter than the time practically required to reach steady state in the above spill model, one obtains due to the monotonicity of the function f ðxÞ ¼ expðxÞ 1=x:
exp Ts 1 T s ( ) ðexpðTs 1 E T 1þ C ¼ Q s C Cs
<
ðexpð4Þ 1Þ 0 4
E < 0:8 0 Q
(8)
< 0:8
Therefore, within the above modeling framework and under the above conditions, the use of the steady-state value Cs (as in (Lee, 2002)) instead of the time-average concentration C in a risk assessment framework would unnecessarily overestimate the associated risk, since the dynamic (transient) features of the vapor concentration profile (which obviously become more important in cases with short exposure times) would be overlooked. The main ideas guiding the development of a more sophisticated, comprehensive and experimentally validated model for spill incidents involving aqueous solutions in an indoor environment that allows the more realistic integration of time-varying evaporation rates (particularly monotonically decreasing evaporation rates due to the decreasing concentration profile of the solute in the spilled liquid (Guo, 2002; Guo et al., 2008)) into its structure have been introduced in the excellent work (Guo et al., 2008). The proposed model is a fourth-order linear dynamic process model comprised of four mass balance equations for the mass of the aqueous solution spilled W, the water vapor concentration in the air m, the solute concentration in the spilled liquid CL and the solute concentration in the air C (Guo et al., 2008):
dW dt dm V dt dC VL L dt dC V dt
¼ Rw Rs ¼ Rw þ Q ðmout mÞ ¼ Rs ¼ Rs QC
ð9Þ
where V is the volume of the enclosed area, VL the volume of the aqueous solution remaining on the floor, Rw ¼ Akgw(msat m) is the rate of water evaporation for the spilled liquid with A being the spill area (time-varying), kgw the gas-phase mass transfer coefficient for the solute, msat the saturated water vapor concentration in indoor air, Rs ¼ AKOL ðCL C=HÞ is the rate of solute emission from the
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spilled liquid (obviously time-varying) with KOL being the overall liquid-phase mass transfer coefficient, H Henry’s constant, and finally mout the water vapor concentration in ambient air and Q the air change flow rate. The set of initial conditions that accompanies the above set of dynamic model equations is: (W(t ¼ 0), m(t ¼ 0), CL (t ¼ 0), C(t ¼ 0)) ¼ (W0, mout, CL0, 0), where W0 is the mass of aqueous solution spilled and CL0 the initial solute concentration in the spilled liquid. Under the assumptions that (Guo et al., 2008): i) the water evaporation rate is considerably larger than that of the solute, ii) the moisture content of the indoor environment, i.e. m is approximately constant (supported by experimental evidence (Guo et al., 2008)), iii) the concentration of the solute in indoor air is much lower than its equilibrium concentration (CL > > C/H), the above dynamic equations can be analytically integrated leading to the following time-varying dynamic concentration profile of the solute in the air (Guo et al., 2008):
CðtÞ ¼
A0 KOL CL0 ðexpð NtÞ expð qtÞÞ Vðq NÞ
(10)
where N ¼ Q/V is the air change rate, and q ¼ ðA0 kgw msat ð1 rÞ=W0 Þ þ ðKOL =qÞ, with q ¼ VL/A being the liquid film thickness (considered constant; for a justification please see (Guo et al., 2008)), A0 being the initial spill area and r the relative humidity in indoor air (m/msat). Within the above modeling framework, please notice that the evaporation rate is a monotonically decreasing quantity (Guo et al., 2008):
K t Rs ¼ AKOL CL0 exp OL
q
(11)
and consequently, the concentration C(t) asymptotically approaches the zero value in agreement with the intuitively expected behavior under realistic conditions. Furthermore, one can show that the above concentration profile attains a maximum value given by the following expression:
Cmax
A K C ¼ 0 OL L0 Vðq NÞ
( N q ) N qN N qN q q
K ¼ CT
(14)
where C is the exposure concentration, T the exposure time and K a constant related to a specific level of fatalities in a population. Haber’s law suggests that fatal health responses by members of a population remain essentially invariant for various exposure scenarios as long as the product CT stays constant: reducing the exposure time by half while doubling the exposure concentration value would lead to the same level of toxicity risk and similar health responses. Quite often the product CT is known as the toxic load and denoted by: L ¼ CT (this symbol will be retained throughout the present paper to denote toxic load), or the “infinitesimal” dL ¼ C(t) dt (toxic load in differential form) whenever the concentration profile is time-varying. Indeed, Haber’s law was also used in cases where concentration profiles were not necessarily constant, with C in the original form (14) being now replaced by the time-average concentration C (Hilderman et al., 1999). The rationale behind such a use, is that the total toxic load under Haber’s law in the case of time-varying concentrations (and hence the associated health effects) remains invariant:
Z L ¼
0
T
Z dL ¼
0
T
CðtÞdt ¼ CT
(15)
However, new experimental studies, toxicological observations and empirical findings elucidated the inherent limitations of Haber’s law (ten Berge et al., 1986; Hilderman et al., 1999; Ride, 1984):
(12)
For this particular spill model, a time-average exposure concentration value C can be analytically computed as well:
Z 1 T CðtÞdt T 0 A K C 1 1 ¼ 0 OL L0 ½expðqTÞ 1 ½expðNTÞ 1 Vðq NÞT q N
to exposure to toxic chemicals have early moorings in the tumultuous scientific career and tragic personal life of Fritz Haber who was the architect of the development of the chemical weapons program of the German army in early 20th century. On the basis of preliminary evidence accumulated through the use of poison gases for military purposes, Haber postulated that fatal toxicity can be described through the following simple law (Andersen, 2003; ten Berge et al., 1986; Hilderman et al., 1999; Holland & Sielken, 1993; Ride, 1984):
C ¼
(13)
which can be considered as a measure of exposure concentration in risk assessment studies. 3. The proposed toxicity risk assessment method Traditionally, toxicological experiments have been conducted in such a way that laboratory animals are exposed to constant concentration levels of the toxic chemical under consideration for a fixed period of time and the corresponding number of fatalities is observed and recorded (Andersen, 2003; Holland & Sielken, 1993; van Leeuwen & Hermens, 1995). From a practical point of view, the selection of the number of fatalities as a health end-point in toxicological studies of this nature is justified since less severe effects on health, even if observed, can not be easily quantified and are inherently associated with significant variability within a certain population (Andersen, 2003; Hilderman et al., 1999; Holland & Sielken, 1993; van Leeuwen & Hermens, 1995). Historically, acute toxicity studies and mortality rates due
i) Regardless of how low the exposure concentration levels are, fatalities should be observed as long as the exposure time becomes quite large. This prediction of Haber’s law leads to overestimating the health effects at low concentration levels, a prediction empirically refuted and theoretically weak since it overlooks the underlying physiological mechanisms associated with recovery processes. ii) The health effects due to high exposure concentration levels can be modulated by shortening the exposure time. This prediction of Haber’s law leads to underestimating the severity of health effects often observed in acute toxicity episodes due to the underlying complexity of the physiological mechanisms activated in order to cope with an “overwhelming” short exposure to high toxic concentration levels. In light of i) and ii), toxicologists introduced nonlinear generalizations of Haber’s law which attain the following form (ten Berge et al., 1986; Hilderman et al., 1999; Ride, 1984):
L ¼ CnT
(16)
where the exponent n is associated with the particular chemical and customarily determined through experiments (with typical values n 1). Notice that the above nonlinear generalization of Haber’s toxic load is in agreement with the empirical evidence in cases i) and ii), i.e. the behavior of toxic load realistically expected under low and high exposure concentration levels. As before, in the case of time-varying concentration profiles one could use the
N. Kazantzis, V. Kazantzi / Journal of Loss Prevention in the Process Industries 23 (2010) 719e726
time-average exposure concentration value C in the above nonlinear generalization: n
Lm ¼ C T
(17)
and thus introduce the notion of a “mean” toxic load for the exposure duration. Notice however that in the nonlinear case n > 1 (as opposed to the linear one where n ¼ 1) the dynamic changes in C ¼ C(t) do matter, and the overall or total toxic load which is properly defined as follows:
Z Lt ¼
T
0
Z dL ¼
T
0
C n ðtÞdt
(18)
( Qn ðC1 ; .; Cm Þ ¼
m 1X Cn m i¼1 i
Z Lt ¼
T
0
Z dL ¼
0
T
n
C n ðtÞdt C T ¼ Lm
(19)
thus representing a quite useful upper bound on toxic loads when evaluating toxicity risk and associated health effects such as fatalities. At this point, a mathematical justification is provided of the above result. Consider the standard Riemann representation of the integral in (18):
Lt ¼ lim
m/N
m X i¼1
Cin ðDtÞ
(20)
under a partition of the exposure interval with mesh: ðDtÞ ¼ T=m and Ci ¼ C(ti) with ti ˛½ðT=mÞi; T=mði þ 1Þ. Similarly, under the same Riemann partition, one obtains: n
Lm ¼ C T ¼
1 T n1
(Z
)n
T
CðtÞdt 0
¼
1 T n1
( lim
m/N
m X
)n Ci ðDtÞ
i¼1
(21) Define now the quantity:
)1 n
(22)
with C1, ., Cm > 0. Notice that:
Q1 ðC1 ; .; Cm Þ ¼
m 1X C m i¼1 i
(23)
Using the generalized mean inequality for n > 1 (Hardy, Littlewood, & Pólya, 1988), the following inequality can be established:
)1 ( n m m P P 1 1 Qn ðC1 ; .; Cm ÞiQ1 ðC1 ; .; Cm Þ0 m Cin > m Ci 0 i¼1 i¼1 ( )n ( )n m m m m X X 1X 1 X ðDtÞn Cin > n Ci 0ðDtÞ Cin > C 0 i m i¼1 m ðmDtÞn1 i ¼ 1 i ¼)1 i¼1 ( ( )n n m m m X X X Pm 1 1 n n Ci ðDtÞ 0 lim Ci ðDtÞ n1 lim Ci ðDtÞ 0Lt Lm i ¼ 1 Ci ðDtÞ > n1 m/N m/N T T i¼1 i¼1 i¼1
is not equal to (17) any more: Lt s Lm. In the special case of a constant concentration profile where C ¼ C(t) ¼ M ¼ constant, then, even in the nonlinear case (n > 1), C ¼ M and Lt ¼ MnT ¼ Lm. The reader is reminded that in a typical toxicological experiment the exposure concentration profile C is constant by design, and therefore, no particular concern is caused about the choice and use of the proper toxic load model. In a spill incident however, the exposure concentration C is realistically expected to vary with time (within the exposure time-window), and the selection of total toxic load (18) is regarded as more useful since it captures the simultaneous effect of nonlinear and time-varying exposure concentrations on toxicity (ten Berge et al., 1986; Hilderman et al., 1999; Ride, 1984). From a risk assessment, as well as regulatory perspective, it is also important to show that in the nonlinear case where n > 1, the total toxic load Lt is larger than the mean toxic load Lm:
723
(24)
Motivated by the ideas introduced in (Hilderman et al., 1999), one should acknowledge that the notion of overall/total toxic load (18), despite its advantages, still lacks a degree of realism when used for the assessment of toxicity risks in a real exposure scenario following a spill incident such the ones under consideration. Indeed, the recognition that it does not capture the undeniable facts that: A) the uptake of any exposure concentration can not be instantaneous but rather one needs to consider an effective exposure concentration or dose available at the receptor site which potentially influences health effects estimates (the number of fatalities in our case), and B) the underlying biological recovery processes do contribute to the health response of a population to toxic exposure, and that toxic loads can not increase indefinitely as time progresses and effective concentration levels become quite low. Apparently, a scientifically thorough and detailed description of cases A) and B) would require the development of a comprehensive and quite often complex physiologically based pharmacokinetic model that by itself could pose considerable challenges (considering all possible exposure routes, metabolic pathways, the fate of the chemical inside the body, etc. which inevitably introduce a large number of parameters that need to be reliably estimated) (Andersen, 2003; Hilderman et al., 1999; Holland & Sielken, 1993; Ramaswami et al., 2005). Instead, as the authors show in (Hilderman et al., 1999), a simple first-order dynamic description of an effective exposure concentration Ceff available at the receptor site could be introduced, and its relationship to the concentration C of the toxic vapor (obtained from a spill model) represented by:
dCeff 1 C Ceff ¼ sup dt
(25)
where sup is an empirical parameter called the uptake timeconstant. Notice that small uptake time-constants sup /0 lead almost instantaneously to: Ceff /C, whereas very large ones
724
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sup /N to Ceff /0 as intuitively expected. For any finite value 0 < sup < N, one also concludes that asymptotically
limt/N Ceff ¼ C. In this case it is of course presupposed that the exposure period T is quite large: T > > 4sup, otherwise, if T < 4sup, then Ceff has not yet converged to C. This behavior is certainly expected, since the above simple dynamic model nicely captures the fact that the uptake process is not instantaneous and the short exposure duration does not allow enough time for the effective concentration level Ceff at the receptor site to reach C the concentration of the toxic vapor. Finally, it should be pointed out that a more detailed uptake model based on “first-principles” would have to integrate all possible exposure and absorption routes (inhalation path involving nose, throat and lungs in which case Ceff is the concentration in the airways, metabolic paths involving the bloodstream, absorption and transfer mechanisms between the lungs and blood in which case Ceff is the concentration in the bloodstream, etc.) (Andersen, 2003; Hilderman et al., 1999; Holland & Sielken, 1993). On the basis of the notion of effective exposure concentration Ceff, the notion of overall/total toxic load can be modified as follows:
Z Leff ¼
T 0
Z dL ¼
T 0
n Ceff ðtÞdt
(26)
by introducing an effective toxic load Leff through which the assumption of instantaneous uptake is relaxed. With respect to case B), one should also be cognizant of the role of complex underlying biological mechanisms (metabolic degradation of the chemical’s toxicity, excretion mechanisms, physiological repair of damaged tissue) responsible for recovery processes as evidenced by numerous studies (Andersen, 2003; Hilderman et al., 1999; Ramaswami et al., 2005). These of course tend to naturally reduce the effective toxic load. In such a case, a simple first-order recovery model for the effective toxic load can be proposed (Hilderman et al., 1999):
dLeff 1 n Leff ¼ Ceff sr dt
(27)
where sr is the recovery time-constant. Notice that (27) further generalizes the effective toxic load model of (26):
dLeff n ¼ Ceff dt
(28)
by capturing also the effect of recovery processes. When sr /N (no recovery), the two models for Leff coincide. If sr /0 (immediate recovery), then Leff /0 as expected. In cases where 0 < sr < N, equation (27) describes the expected gradual decline of the effective toxic load values due to the latent recovery processes. Summarizing, in the case of a noninstantaneous uptake the following toxic load model is proposed:
dCeff 1 C Ceff ¼ sup dt dLeff n ¼ Ceff dt
(29)
with Ceff(t ¼ 0) ¼ 0, Leff(t ¼ 0) ¼ 0 and C(t) representing the toxic vapor concentration profile as given by the spill model equations presented in Section 2. In cases where recovery processes are taken explicitly into account, the proposed toxic load model takes the following form:
dCeff 1 C Ceff ¼ sup dt dLeff 1 n Leff ¼ Ceff sr dt
(30)
with Ceff(t ¼ 0) ¼ 0, Leff(t ¼ 0) ¼ 0 and C(t) representing the toxic vapor concentration profile obtained through the spill model equations presented in Section 2. Given the availability of a working spill model and a model for the effective toxic load, the last remaining component of a quantitative toxicity risk assessment framework is the development of a risk model (a type of doseeresponse relationship) that relates the effective toxic load to the number of fatalities (or a percentage) in a population due to exposure to a toxic vapor resulting from a spill incident. At this point, the reader is reminded of the two dimensions of a quantitative chemical risk assessment methodological framework: the “size of risk” as realized through the notion of risk quotient (the ratio of Ceff to a threshold value such as PEL or IDLH), and the “consequences of risk” as realized through the appropriate doseeresponse relationship and a specific health end-point (fatalities for example in toxicity studies). In the context of the present study, a probit doseeresponse model is proposed (Finney, 1971; Hilderman et al., 1999; Holland & Sielken, 1993). According to this methodology the variability of individual tolerances to toxic chemicals is recognized (Holland & Sielken, 1993). In particular, it is assumed that a certain threshold dose or toxic load Leffth exists for each individual, but such a threshold toxic load value varies amongst the members of a population. Furthermore, it is assumed that the individual threshold toxic load Leffth is log normally distributed with a certain logarithmic mean m and standard deviation s (an assumption owing its justification to experimental findings and empirical data (Hilderman et al., 1999; Holland & Sielken, 1993)). Therefore, the expected percentage of fatalities P due to exposure to a certain toxic load Leff would be determined by a threshold load that satisfies the inequality: Leffth < Leff, and thus given by the cumulative distribution function shown below:
1 P ¼ pffiffiffiffiffiffiffi 2ps
Z
(
lnLeff
N
exp
) 1 xm 2 dx s 2
(31)
The above expression (31) can be rewritten through a standard change of variables as follows (Finney,1971; Holland & Sielken,1993):
Z aþblnLeff
1 1 P ¼ pffiffiffiffiffiffiffi exp y2 dy ¼ F a þ b ln Leff 2 2p N
(32)
where F is the standard normal integral (Finney, 1971). One now defines the probit variable Pr:
Prha þ bln Leff
(33)
and therefore:
P ¼ FðPrÞ
(34)
Notice that a, b coefficients in the above change of variables in integral (32) are related to (m, s) of the above health response distribution, depend on the specific chemical and are determined in practice through experiments and on the basis of empirical data. For a specific value of the effective toxic load Leff, equation (33) gives the associated value of the probit variable Pr, and finally the percentage of fatalities is obtained by using equation (34) (specifically, tabulated values of the standard normal integral corresponding to various values of its argument). Conversely, for a certain percentage of fatalities, one inverts the P ¼ F(Pr) relationship computing the associated value of the probit variable Pr, and then, using equation (33) the corresponding value of the effective toxic load Leff that induces the aforementioned percentage of fatalities is estimated. In the next Section, the proposed toxicity risk assessment method is evaluated through simulation studies in a case study involving a spill episode of ammonia solution in an enclosed area.
N. Kazantzis, V. Kazantzi / Journal of Loss Prevention in the Process Industries 23 (2010) 719e726
4. Illustrative example: toxicity risk assessment for an ammonia spill incident
Table 2 Spill incident II e process parameter values.
Pr ¼ a þ b ln Leff
(35)
with a ¼ 15.8, b ¼ 1, n ¼ 2, since it appears to be in closer agreement with experimental results and methodologically consistent with toxicological requirements involving more realistic health responses of humans to toxic vapors (Schubach, 1995). The 1% fatalities level corresponding to a probit variable value of: Pr z 2.6 is considered that is often related to a toxic load or concentration threshold value close to the Immediately Dangerous to Life and Health Limit (IDLH). Indeed, using equation (33), one can explicitly calculate the corresponding level of effective toxic load: 7 2 3 L[1] eff ¼ 9.7 10 [(mg) (min)/m )] that is probabilistically expected to induce 1% fatalities. In the first case, an acute exposure scenario is considered where immediately after the spill and for a relatively short period of time, the exposure concentration fluctuates drastically attaining a maximum value of: Cmax z 5980 [mg/m3] which is perilously close to levels characterized as severe by various regulatory agencies (Schubach, 1995; U.S. Department of Health and Human Services, 2004), rapidly decreasing afterwards to much lower levels so that the 8-h average concentration value Cz35 [mg/m3] stays close to the “safe” PEL level. In Fig. 1, please notice that the total toxic load model (18) (in this case we consider the simpler model with instantaneous uptake and no recovery denoted by L1) crosses the L[1] eff level that induces 1% fatalities after
Table 1 Spill Incident I e Process parameter values. Process parameters
Values
kgw KOL msat r A0 W0 V N ¼ Q/V
12.5 mh1 4E-3 mh1 18 g3 0.69 20.7 m2 15.4 kg 30 m3 0.4 min1 9.6E-6 m 1E6 g3
q
Process parameters
Values
kgw KOL msat r A0 W0 V N ¼ Q/V
12.5 mh1 4E-3 mh1 18 g3 0.69 0.207 m2 154.3 g 30 m3 0.004 min1 9.6E-4 m 1E4 g3
q
CLO
approximately 5 min, capturing nicely the severity of the underlying acute exposure scenario. This behavior is contrasted with a toxic load model based on the 8-h average (mean) concentration value Cz35 [mg/m3], which, as shown in Fig. 1, grossly underestimates the associated toxicity risk. Therefore, this particular case illustrates that it is certainly more advantageous to use even the simple total toxic load model (18) in spill incidents, when compared to more traditional models that use time-average (mean) or other constant exposure concentration values. In the second case, a different spill incident is considered under conditions close to the experimental ones reported in (Guo et al., 2008). In this case, the exposure concentration fluctuates mildly within a larger exposure window reaching a maximum value of Cmax z 60 [mg/m3]. This is certainly a case of negligible toxicity risk since all concentration values remain close to the PEL value, and the standard regulatory characterization of ammonia toxicity under these conditions is practically risk-free. The proposed effective toxic load model (30) was used in our simulation studies with an uptake time-constant sup ¼ 1[s] (a reasonable value under the assumption that the uptake rate is determined by the inhalation rate in similar cases as justified in (Hilderman et al., 1999; U.S. Department of Health and Human Services, 2004)) and a recovery time-constant sr ¼ 20[min] (a reasonable value justified in light of empirical findings and results from experimental studies on underlying physiological, metabolic toxicity reduction and excretion mechanisms involving ammonia as discussed in (U.S. Department of Health and Human Services, 2004)). Based on the simulation results graphically depicted in Fig. 2, notice that the proposed
8
10
6
10 Load (mg/m3)2 min
An aqueous ammonia solution conforming to the specifications of the one used in the experimental study (Guo et al., 2008) is considered (1.3% (w/w) concentration) and spill episodes are simulated with the aid of the second model presented in Section 2. In all the ensuing simulation runs all mass transfer coefficient values as well as inherent physicochemical properties of the ammonia solution are the same as the ones considered in the experimental investigations in (Guo et al., 2008) that were conducted in order to validate the associated spill model. The rest of the model input variables such as the enclosure volume, ventilation rate, initial concentration of the aqueous solution, amount of solution spilled, initial spill area could vary giving rise to different scenarios. For the particular cases or spill incidents considered in the present study the above sets of model input values are tabulated and presented in Tables 1 and 2. It should be also pointed out that in both the above scenarios which physically correspond to drastically different spill episodes, the same 8-h average (mean) concentration value Cz35 [mg/m3] is considered, a value close to the Permissible Exposure Limit (PEL) value as set by OSHA (U.S. Department of Health and Human Services, 2004). Furthermore, the probit doseeresponse model equation used for the ammonia solution was the one developed by the Netherlands Organization of Applied Scientific Research (TNO):
CLO
725
4
10
2
10
L1 (instantaneous) L(1% fatalities) Load (mean)
0
10
−2
10
−1
10
0
10
1
10
t[min] Fig. 1. Spill incident I: Toxic load versus time curves.
2
10
726
N. Kazantzis, V. Kazantzi / Journal of Loss Prevention in the Process Industries 23 (2010) 719e726
provides the requisite degree of differentiation between the exposure concentration obtained through the aforementioned models and the effective concentration that reaches the receptor site as determined by a finite uptake rate of the toxic vapor/gas. Furthermore, on the basis of the time-varying effective concentration, an effective toxic load that takes into account latent recovery processes was integrated into a probit methodological framework within which the quantification of a population response to toxic exposure was made possible. Finally, the proposed method was evaluated in a case study involving a spill episode of ammonia solution in an enclosed area.
5
5
x 10
L1(effective) L2(instantaneous) L3(mean)
4.5 4
Load (mg/m3)2 min
3.5 3 2.5 2 1.5
Acknowledgements
1 0.5 0
0
50
100
150
200
250
300
350
t[min] Fig. 2. Spill incident II: Toxic load versus time curves.
The authors would like to thank Professor S. M. Mannan and his Associates at the Mary Kay O’Connor Process Safety Center, Department of Chemical Engineering, Texas A&M University for their kind invitation to participate in the 2009 International Process Safety Symposium. They are also indebted to the anonymous reviewers for their thoughtful suggestions and helpful remarks. References
effective toxic load (denoted by L1) has the capacity to realistically capture the very low risk level under the set of conditions associated with the particular spill incident considered in this case. However, in such a case, both the toxic load with instantaneous uptake and no recovery (denoted by L2), as well as the toxic load based on the 8-h average (mean) concentration value Cz35 [mg/m3] predict unreasonably high risk levels, i.e. after a certain exposure period they both cross the L[1] eff level of 1% fatalities, thus contradicting the established safety threshold values and limits (such as PELs) which are deliberately set by regulatory authorities in a conservative precautionary manner, and certainly orders of magnitude below any fatalities-producing exposure concentration levels. Therefore, as shown in this second case, the proposed quantitative toxicity risk assessment method appears to carry considerable merit when comparatively evaluated against more traditional ones in pertinent studies. 5. Concluding remarks A new method for the assessment of toxicity risk due to spill episodes involving volatile liquid hydrocarbons and aqueous solutions in enclosed areas was proposed. Source models with timevarying evaporation and emission rates were used in conjunction with appropriate mass transfer models to estimate dynamic concentration profiles of potentially toxic pollutants following spills of volatile liquid hydrocarbons as well as aqueous solutions in an indoor environment. Relaxing the assumption found in more traditional approaches to toxicity risk assessment where toxic loads are estimated under constant concentration levels of the toxic pollutant, it was shown that the proposed approach takes explicitly into account the dynamic features of the concentration profile during the time of exposure. Furthermore, the proposed method incorporated the idea of using a simple dynamic description that
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