Probabilistic and Monte Carlo Risk Models for Carbon Nanomaterial Production Processes

Transcription

1 Probabilistic and Monte Carlo Risk Models for Carbon Nanomaterial Production Processes Zeynep D. Ok, Jacqueline A. Isaacs, and James C. Benneyan Abstract Given considerable uncertainty surrounding the occupational, consumer, and environmental, health and safety (EHS) risks of various nanomaterial manufacturing processes, modeling their relative risks and benefits is especially important. This paper discusses possible risk assessment methods that might be useful in such applications and explores three probabilistic approaches in greater detail: Monte Carlo (MC) simulation models, Bayesian belief networks, and multi-criteria decision trees. These approaches are illustrated for single wall carbon nanotubes (SWNT) produced via high pressure carbon monoxide (HiPco) processes to study the impact of inherent uncertainties and early EHS standards decisions on predicting long-term manufacturing costs, occupational health (OH) exposure risks, and associated tradeoffs. Until research progresses on the EHS risks of nanomaterials, these types of analyses can provide useful information for private and regulatory decision-makers and for guiding research priorities. Index Terms HiPco, occupational health risk, SWNT, uncertainty I. INTRODUCTION S commercialization of nanotechnology is proceeding Aquickly in the global market, the need for research to more fully understand the occupational, consumer, and environmental, health and safety (EHS) risks of nanotechnology has grown. There are indications that engineered nanomaterials may have negative properties that might presents risks to human health [1]. Critical reviews on the toxicity of single wall carbon nanotubes (SWNTs) showed damage to lung tissue in mice [2], [3], but further research is needed to develop more definitive information about EHS risks of nanotechnology. In the Nanotechnology White Paper, U.S. Environmental Protection Agency has announced its intent to develop roadmap for assessment of EHS risks of nanotechnology [4]. A recent study undertaken by the National Institute for This work was supported by National Science Foundation grants SES and EEC through the Nanoscale Science and Engineering Center for High-rate Nanomanufacturing. J. A. Isaacs is with Mechanical and Industrial Engineering Department, Northeastern University, Boston, MA USA. (corresponding author phone: ; jaisaacs@coe.neu.edu) Z. D. Ok is with Mechanical and Industrial Engineering Department, Northeastern University, Boston, MA USA. ( zeynep@coe.neu.edu) J. C. Benneyan is with Mechanical and Industrial Engineering Department, Northeastern University, Boston, MA USA. ( benneyan@coe.neu.edu) Occupational Health has suggested preliminary guidelines for working safely with nanomaterial [5]. Even though attention to EHS issues related to this emerging technology has increased, and a strategy for EHS research was announced [6], the risks of nanotechnology are likely to remain unclear for the foreseeable future since the research to definitively characterize risk, and provide guidance for safe handling of nanomaterials, will require some time. Several probabilistic, multi-criteria, and deterministic methods exist in the literature for informing decisions made in various contexts under significant uncertainty or with multiple criteria. The applicability of each of these methods somewhat depends on the nature of the problem and research questions. Table 1 summarizes some of these methods that may have potential utility for risk analysis of nanomaterials and various nano-specific processes, potentially including Monte Carlo simulation models, decision trees, Bayesian belief networks, influence diagrams, multi-criteria decision making, analytic hierarchy process, goal programming, desirability functions, and life cycle assessment. TABLE I. Method Monte Carlo models Decision trees Bayesian belief networks Influence diagrams Multi-criteria decision making Analytic hierarchy process Goal programming Desirability functions Life cycle assessment SUMMARY OF POSSIBLE RISK ASSESSMENT METHODS FOR NANOMATERIALS Pros & Cons + Allows modeling uncertainty - No tradeoff framework + Allows insights with limited data - Can become overly complex + Means for calculating conditional probabilities - No decision nodes + Accounts for relationships - Compact representation + Tradeoff frontiers - Deterministic + Practically useful - Based on subjective opinions + Can handle relatively large number of objectives - Deterministic + Can compare discrete alternatives, robust - Abstract approach, arbitrary weights + Systematic tool - Comparison of different studies is difficult. Given the inherent uncertainties described above, the current paper explores the use of three probabilistic risk assessment tools Monte Carlo models, Bayesian belief networks, and decision trees although other approaches will be explored in future work. The use of Monte Carlo simulation models are illustrated below with an example that investigates high pressure carbon monoxide (HiPco) carbon nanotube

2 production processes. In such models, uncertainties in the level and timing of possible required standard practices and associated full-scale production cost and occupational health exposure risk values are represented by probability distributions and chance events. Bayesian belief networks and decision tree analysis are additional methods that can be used to model, investigate, and compare uncertainties and alternatives in worker health and safety protection investment decisions. Given the significant uncertainty in commercialization of nanotechnology, any of these models can allow development of a more informed understanding of tradeoff decisions and the impact of inherent cost and occupational health uncertainties. II. DESCRIPTION OF METHODS A. Monte Carlo Models Monte Carlo simulation models are widely used in risk assessment because they can capture very realistic levels of complexities of process logic, chance events, and probabilistic outcomes. Once developed, they can be run on a wide range of scenarios and can be used to provide several types of analysis results. Random sampling typically is used to obtain values of non-deterministic variables used within the model, such as costs, implementation rates, compliance, health impact, and so on. Fig. 1 summarizes the general logic of a Monte Carlo model developed to study long-term HiPco SWNT occupational health risks, manufacturing costs, and inherent tradeoffs. Results of MC models here included the expected values, standards deviations, and probability distributions of production costs and occupational health exposure. B. Bayesian Belief Networks Bayesian belief networks graphically represent probabilistic relationships in a risk model and are used in combining multiple models, studies, or expert opinions in a rational manner [7]. Such models have been used in numerous application areas including bioinformatics, medicine, engineering, and law [8-11]. In a Bayesian network, only uncertain variables and their dependencies are modeled. Since the current data are not complete regarding EHS risks of nanomaterials and nanotechnology processes, Bayesian networks can be useful tools to combine multiple expert opinions, preliminary studies and models analytically. A Bayesian network can be transformed to a decision tree by expanding uncertainty nodes with decision nodes. Fig. 2 illustrates an example of a simple four-node Bayesian network. Fig. 2. Four-node Bayesian network representation. Fig.1. Monte Carlo logic flow. C. Decision Trees Decision trees are graphical representations of all decisions and their possible outcomes, including associated uncertainties in a risk model, and provide a useful graphical overview of all stages in a multistage decision problem [12]. Square nodes represent the decision analysis points by showing all available distinct options for a decision maker at that stage. Circular nodes represent circumstances with uncertain outcomes, and each path from left to right leads to some specific end results and outcomes. As an example, Fig. 3 illustrates all elements (i.e., decisions, uncertainties, and outcomes) of a decision problem modeled for a nanomanufacturing facility, with 4 different investment level options for worker protection and various uncertainties associated with EHS risks. After the first stage decision of worker protection investment level, the decision-maker faces EHS risk uncertainty at three levels (i.e., nanomaterials found to be non-toxic, moderately toxic, or extremely toxic). Outcome alternatives can be represented as expected possible manufacturing costs and occupational health exposure based on the decision path chosen.

3 By working through the decision options and chance events with conditional probabilities, the expected outcome(s) and variances (and confidence intervals) for each tree path can be estimated and used to make informed decisions. Although basic decision trees are limited to the optimization of a single objective, many real world problems involve multiple (and conflicting) objectives. Multi-objective decision tree analysis methods therefore have been developed as an extension of the single objective based decision tree analysis [13] and could be useful in this context, such as for comparing risks and production costs. protection, the likely occupational exposure is assumed to be 9 units, whereas under low, medium, or high levels, these become 8, 4, and 1 unit, respectively. TABLE II. EHS Standards Level ASSUMED PARAMETERS FOR COST ($/G) AND EXPOSURE TRIANGULAR DISTRIBUTIONS Costs (Exposure) (0 to 10 scale) Minimum Most Likely Maximum None $405 (7) $450 (9) $495 (10) Low $414 (6) $460 (8) $506 (9) Medium $475 (3) $528 (4) $581 (6) High $594 (0) $660 (1) $726 (2) TABLE III. ASSUMPTIONS FOR EHS TRANSITION PROBABILITIES EHS Standards Transition Probabilities (to) Level (from) None Low Medium High None Low Medium High Fig. 3. Example of a decision tree for a nanomanufacturing facility. III. EXAMPLE OF A MONTE CARLO NANO-RISK MODEL A. Model Logic Ok, Isaacs, and Benneyan [14] developed a MC model to assess the OH risks and production costs of SWNT HiPco processes associated with possible regulatory futures. Four general levels of occupational exposure control standards (i.e., none, low, medium, and high) were defined to represent the spectrum of possible nano-ehs standards, with Table 4 summarizing cost assumptions for each level. A process-based technical cost model [15] was developed and used to determine baseline cost estimates for arc ablation ($1,830/g), chemical vapor deposition ($1,586/g), and HiPco ($450/g) SWNT manufacturing processes, all assuming 50% synthesis reaction yield, 90% purification yield, no EHS standards, and 10,000 g/yr production volume (Table 2). If low, medium, or high levels of EHS standards are adopted, the HiPco production costs increase progressively to $460/g, $528/g, and $660/g, respectively, with Fig. 4 comparing these costs for other production volumes. Variability and uncertainty in implementation costs and exposure amounts at each EHS level are represented by triangular distributions (Table 2), with the minimum and maximum possible costs at each EHS level set equal to ±10% of their respective baseline costs. Since no data are readily available regarding OH exposures for the HiPco SWNT manufacturing process, exposure is represented by an arbitrary 0 to 10 scale. For example, if a company uses no worker Fig.4. Comparison of HiPco production costs for each level of EHS standards. As the Monte Carlo model executes, manufacturing costs and occupational exposure amounts are randomly generated from these probability distributions, with the model logic implemented in such a way to ensure that manufacturing cost decreases and exposure increases as higher levels of worker protection are implemented. Table 3 summarizes possible implementation assumptions for year-to-year probabilities of moving from one level of protection to some higher level, although these can be changed to any values, since they are highly dependent on technology, research on health risks, and political forces. For example, the likelihoods of remaining at no standards level and imposing low level standards are equally high (0.475), whereas probabilities of imposing medium, or high levels of EHS standards are equally low (0.025). If a low level of standards is imposed in some future year, the probability of remaining at this low level of protection in subsequent years again will be higher (0.9) than of transitioning to medium or high level standards (0.05) as shown in the second row of

4 TABLE IV. SUMMARY OF ASSUMPTIONS FOR EHS STANDARDS Engineering Controls General Exhaust - Ventilation Fume hoods Enclosure of processes Administrative Controls Annual worker training Air monitoring Medical monitoring Personal Protective Equipment** Level of EHS Standards None Low Medium High 24 hours, 1,000 cfm ventilation rate, $10,000 capital cost, $3,000/year operating cost 8 hours of training, $560/year instructor cost Monthly monitoring, equipment cost of $20,000 Gloves Latex 5 pairs/shift, $0.06/pair 24 hours, 1,000 cfm ventilation rate, $10,000 capital cost, $3,000/year operating cost $4,000 capital cost for 6.25 ft 2 equipment and $9,500 for 25 ft 2 equipment * 8 hours of training, $560/year instructor cost Weekly monitoring, equipment cost of $20, hours, 1,000 cfm ventilation rate, $10,000 capital cost, $3,000/year operating cost $4,000 capital cost for 6.25 ft 2 equipment and $9,500 for 25 ft 2 equipment * 50% decrease in labor productivity, 50% extra equipment cost 8 hours of training, $560/year instructor cost Biweekly monitoring, equipment cost of $20,000 $950/worker/year Nitrile 5 pairs/shift, $0.09/pair 5 pairs/shift, $0.09/pair Respirators Disposable 1/shift, $0.70 1/shift, $0.70 HEPA filters 1 pair/ 30 hrs, $10/pair Tyvek suits 1/shift, $4 *** Table 4. Similarly, if a medium standards level is introduced, the probabilities of remaining at this level in the next year, or of moving to a high level, both are This transition logic is repeated annually for a user-specified period, taken to by a 10-year analysis period in the results below. B. Potential Results from MC Risk Models Using the above assumptions, 10,000 MC replications of a 10-year analysis window resulted in expected values and standard deviations of $528/g and $65/g for manufacturing cost and 5.6 units and 2.3 units for exposure for HiPco SWNT manufacturing processes. Note that in this type of analysis, the expected value and standard deviation correspond to the most likely one-time outcome and the uncertainty in this one-time outcome, respectively (rather than, say, the range of many outcomes that would be experienced over time). In this example, the exact manufacturing cost is anywhere between roughly $405/g and $726/g (a range of $321) and the exact units of exposure is anywhere between 0 and 10 units. Of course, such large ranges, due to the amount of uncertainty, are of marginal value and further analysis can be conducted to try to reduce these results (demonstrated below). Moreover, since production costs and occupational exposure are likely to be significantly correlated, further simulation analysis can be conducted to help develop a better understanding of the relationship between the two. For example, Fig. 5 and Fig. 6 illustrate the joint probability distribution, amount of correlation, and inherent tradeoff between cost and exposure, with the probability of having lower workplace exposure decreasing as the production cost decreases (r = ). Given the current significant uncertainty regarding required standards, costs and occupational health risks, similar analyses could be performed under different sets of assumptions to provide further insight for informing decision-making, initial plant design, and technology investments. Fig. 5. Joint probability density of HiPco SWNT manufacturing costs and exposure.

5 Fig. 6. Correlation of 10-year annualized cost and OH exposure IV. OTHER RELATED APPROACHES A. Trade-off Analysis The study can be expanded to further analyze the tradeoffs between manufacturing costs and exposure. An example from an earlier study [14] is given in Fig. 7 where two performance measures, cost, C, and exposure, E, are combined into some type of expected total cost function, T. In the total cost function, T = C+kE a, k represents the per gram cost of one unit of annualized exposure, and values of a > 1 or a <1 result in increasing or decreasing exposure costs (respectively) as exposure increases. Fig. 7 illustrates the expected total costs for different a and k combinations. Fig. 7. Examples of the expected value of total cost (production plus exposure costs), for the case where T = C+kE a B. Use of Experimental Designs Design of experiments (DOE) factorial screening and response surface methods can be used with any of the above model approaches to provide further insight into the impact and strength of relationships between various process dynamics. DOE may be especially helpful, given the extreme amount of uncertainty and its impact on the inability to predict the long-term production costs and occupational health exposure, in order to analyze and identify which factors most affect the uncertainty in model results (i.e., production costs, and exposure). In the simplest approach, 2 k factorial designs are particularly useful to estimate design factors for process development. In the MC risk model, for example, the design factors might include transition probabilities, the mean cost and exposure, and cost and exposure standard deviations under each level of EHS standards. Tables 5 and 6 summarize the design settings, column assignments, and four-performance measure responses (i.e., cost mean, cost variance, exposure mean, and exposure variance) of a recent DOE analysis, with 10 responses (of 10,000 replications each) generated for each experimental run. The slight loss of balance and orthogonality in the design became necessary because of the consistency logic mentioned in section 3 to ensure non-decreasing cost and non-increasing exposure amounts within each 10-year replication, with resultant half-effect sizes and p values therefore computed via stepwise regression. Results indicate that X 5 (EHS implementation probabilities) is the largest contributor to the cost and exposure means and variabilities with value of p = 0. Setting TABLE V. Transition Probabilities LOW AND HIGH POINT ASSUMPTIONS Cost SD Exposure SD -1 50% slower 5% of current 5% of current 0 current current current 1 50% faster 15% of current 15% of current C. Influencing the Research Agenda Given the significant uncertainty regarding the health risks of nanomaterials, use of these types of analyses can provide useful information for manufacturers, policy makers, and researchers to make informed decisions and research investments. For example, DOE can be used as described above to identify which factors and uncertainties have the greatest impact on uncertainty in results, with the implication that investment of time and money in these areas would lead to the greatest ability to make informed decisions. In the case of the MC risk model and DOE study described above, the results (Table 6) suggest that developing better estimates first for the likelihoods of future EHS requirements and then for the production costs and risks under low and high standards would result in the greatest reduction in the uncertainty of occupational health risks and production costs. Uncertainty in EHS requirement probabilities is by far the biggest contributor to all four responses (mean and SD of cost and exposure) by a factor of 2 to 4, whereas the largest contributors to cost uncertainty include σ Cost,Low and to a lesser extent, σ Cost,High, while σ Exposure,None is the largest contributor to exposure uncertainty. Interestingly, the effect of uncertain costs and exposures at medium levels of standards drops out of all models. Because the risks of commercializing nanotechnology are likely to remain unclear for some time, these types of methodologies can provide insights for defining the priorities of a research agenda.

6 TABLE VI. EXAMPLE OF EXPERIMENTAL DESIGN RESULTS Cost / Exposure Uncertainty Levels Transition Responses (n = 10) σ None σ Low σ Medium σ High Probabilities Cost Exposure Runs X 1 X 2 X 3 X 4 (X 1X 3) X 5 (X 1X 2X 3) Y 1 Mean Y 2 Variance Y 3 Mean Y 4 Variance Cost mean E(C): Y 1 = X X 5 p value Cost variance V(C): Y 2 = X X X 5 p value Exposure mean E(E): Y 3 = X X *X 5 p value Expose variance V(E): Y 4= X X X X 5 p value V. CONCLUSION Assessing economic versus occupational health tradeoffs of nanotechnology is not easy given the high degree of exposure and cost uncertainty. This paper has discussed possible risk assessment models for studying nanomaterial manufacturing processes, including MC simulation models, Bayesian belief networks, and decision trees. Results from the MC risk model example underscore that technology investments, research, and policy decisions should not be based on expected values of costs and exposure amounts alone, given the high level of uncertainty and variability in results. Experimental designs can be used to help identify which current unknowns have the greatest impact on this unpredictability decision uncertainty, and therefore would benefit the most from research investments and efforts. Future work will further explore the use of Bayesian belief networks, multi-criteria decision trees, and other possible risk assessment methods. ACKNOWLEDGMENT The authors thank Dr. Michael Ellenbecker, Director of the Toxics Use Reduction Institute at the University of Massachusetts Lowell for his input on EHS assumptions. REFERENCES [1] NIOSH, "Progress toward safe nanotechnology in the workplace," U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, National Institute for Occupational Safety and Health Publication No , [2] C.-W. Lam, J. T. James, R. McCluskey, S. Arepalli, and R. L. Hunter, "A review of carbon nanotube toxicity and assessment of potential occupational and environmental health risks," Critical Reviews in Toxicology vol. 36, pp , [3] K. Donaldson, R. Aitken, L. Tran, V. Stone, R. Duffin, G. Forrest, and A. Alexander, "Carbon nanotubes: A review of their properties in relation to pulmonary toxicology and workplace safety," Toxicological Sciences, vol. 92, pp. 5-22, [4] EPA, "Nanotechnology white paper," U.S. Environmental Protection Agency, EPA Science Policy Council 100/B-07/001, [5] NIOSH, "Approaches to safe nanotechnology: An information exchange with NIOSH," U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, National Institute for Occupational Safety and Health Version 1.1., [6] NSTC, "Strategy for nanotechnology-related environmental, health, and safety research," The National Nanotechnology Initiative, National Science and Technology Council, Executive Office of the President of the United States, [7] R. T. Clemen and R. L. Winkler, "Combining probability distributions from experts in risk analysis," Risk Analysis, vol. 19, pp , [8] K.-C. W. Liang, Xiaodong; Anastassiou, Dimitris "Bayesian basecalling for DNA sequence analysis using hidden Markov models," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 4, pp , [9] R. Beuscart, V. Froidure, A. Duhamel, and C. Beuscart, "Bayesian networks for antibiotics prescription," Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings, vol. 2, p. 856, [10] T. A. Mast, A. T. Reed, S. Yurkovich, M. Ashby, and S. Adibhatla, "Bayesian Belief Networks for fault identification in aircraft gas turbine engines," IEEE Conference on Control Applications - Proceedings, vol. 1, pp , [11] P. Thagard, "Causal inference in legal decision making: Explanatory coherence vs. Bayesian networks," Applied Artificial Intelligence, vol. 18, pp , [12] Y. Yuan and M. J. Shaw, "Induction of fuzzy decision trees," Fuzzy Sets and Systems, vol. 69, p. 125, [13] Y. Y. Haimes, D. Li, and T. V., "Multiobjective Decision Tree Analysis," Risk Analysis vol. 10, pp , [14] Z. D. Ok, J. C. Benneyan, and J. A. Isaacs, "Risk Analysis Modeling of Production Costs and Occupational Health Exposure of Single Wall Carbon Nanotube Manufacturing," Journal of Industrial Ecology, submitted for publication. [15] M. L. Healy, L. Dahlben and J. A. Isaacs, "Environmental Assessment of Single Wall Carbon Nanotube Processes," Journal of Industrial Ecology, submitted for publication.