**4. Results and discussion**

The MC simulations for evaluation parameter uncertainty involve the following steps [47]:


The REEs can be grouped into two different categories based on their atomic numbers. REEs with atomic numbers 57–63 are classified as light-rare earths (LREEs), and REEs with atomic numbers 64–71 are classified as heavy-rare earths (HREEs) [48]. However, the term "rare" earth is a misnomer; they are relatively abundant in the Earth's crust; however, they are typically dispersed and only rarely occur in concentrated and economically exploitable mineral deposits [49].

The literature on the flotation of monazite is rather scarce. The available literature focused on the separation of monazite from xenotime, bastnaesite, rutile, and zircon [50] or on the Rhône-Poulenc liquid-liquid extraction process for separation of the REEs from monazite [51] and the Shanghai Yue Long Chemical Plant monazite concentrate treatment in the process similar to the Rhône-Poulenc process [11], both described in [49].

Monazite and xenotime from titania-zircon paleo beach placers in Australia, in the 1980s, were the third most important source of REEs in the world [52]. According to [53], in Australia, monazite typically has associated radioactivity due to thorium content (by substitution up to 30%). Until 1995, rare earth production in Australia was largely a byproduct of processing monazite contained in heavy mineral sands [54].

*3.1.2. Data quality and collection*

30 Lanthanides

As noted above, very often LCI required a lot of data [17, 18] that are well correlated to the study context [40]. Data quality is discussed widely in literature [17, 23, 40–44]. In [45] analyzed uncertainty in a comparative LCA of hand drying systems pointed that data collection is one of the limitations in their LCA analysis. The databases presented in this study are affected to several uncertainties. According to [41], the basic uncertainty in data quality considerations of the inventory of rare earth concentrate processes comes out with data obtained from the literature studies. Large uncertainties exist for the infrastructure and also for particle emissions, fresh water use, and land use [41]. Another reason for the uncertainties is the nature of the chemicals used for the recovery of the REEs from the concentrate after flotation and beneficiation processes (e.g., collector, conditioner, depressant) due to production system characterized

by diverse practices and technologies [41, 46], as well as various laboratory methods.

in the study is obtained from the following sources:

• Expert consultations and knowledge of the process

• The subject literature—scientific publications

**4. Results and discussion**

deposits [49].

**2.** Specify properties of each parameters. **3.** Generate data from the distribution.

The primary data used in the study is obtained from the Deliverable D1.2 Report on the physical-chemical properties of available materials for the recovery of REE and Deliverable D1.3 chemical and mineralogical data of secondary REE sources [1]. The secondary data used

The MC simulations for evaluation parameter uncertainty involve the following steps [47]:

**4.** Use the generated data as possible values of the parameter in the model to produce output.

The REEs can be grouped into two different categories based on their atomic numbers. REEs with atomic numbers 57–63 are classified as light-rare earths (LREEs), and REEs with atomic numbers 64–71 are classified as heavy-rare earths (HREEs) [48]. However, the term "rare" earth is a misnomer; they are relatively abundant in the Earth's crust; however, they are typically dispersed and only rarely occur in concentrated and economically exploitable mineral

The literature on the flotation of monazite is rather scarce. The available literature focused on the separation of monazite from xenotime, bastnaesite, rutile, and zircon [50] or on the Rhône-Poulenc liquid-liquid extraction process for separation of the REEs from monazite [51] and the Shanghai Yue Long Chemical Plant monazite concentrate treatment in the process similar

**1.** Select a distribution to describe possible values of each parameter.

to the Rhône-Poulenc process [11], both described in [49].

In addition to Australia, monazite deposits in Brazil, India, Malaysia, Thailand, China, Thailand, Sri Lanka, South Africa, and the United States constitute the second largest segment [49]. Present-day production is from India, Malaysia, Sri Lanka, Thailand, and Brazil [52]. Moreover, approximately 500 t of monazite per year was produced from 1952 to 1994 as a byproduct of titania-zircon production from Pleistocene sands near Green Cove Springs in Florida [52].

The Carolina monazite belt, from which a total of about 5000 t of monazite was produced between 1885 and 1917, has considerable placer reserves that average 0.25 kg/m3 of monazite [55]. Bear Valley, Idaho, where monazite- and yttrium-bearing euxenite was mined by dredging, contains an estimated 10,000 t of REOs along with significant niobium and tantalum, on the basis of data from [56]. At Baotou, the largest producer of rare earths in China, the bastnesite concentrates contain a small amount of monazite [49].

According to ENVIREE project, flotation tests have been carried out on the flotation tailing from New Kankberg to find out if the REEs can be recovered [57]. The results indicate that most of the REEs are in monazite. *Monazite* is the second most important rare earth, after bastnaesite, and is a rare earth phosphate mineral that contains various amounts of thorium [50]. Sample from the flotation tailing was delivered to the ENVIREE project. After delivery of samples and their homogenization, they were analyzed. As mentioned above, ICP-MS analysis of samples was investigated, in order to test the availability of REE extraction. The results are presented in **Table 1** [1].

In this study we concentrate on a set of 16 REEs, denoted as critical [58] (European Commission 2014), namely, Sc, Dy, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Ho, Er, Tm, Tb, Yb, and Lu. MC, an uncertainty propagation method [59], required definition of the mean, type of statistical distribution, and standard deviation (SD) for each parameter [59]. In this study, the uncertainty analysis was modeled using probability distributions considered to be lognormal (term *lognormal distribution*) was derived from [60], according to the criteria proposed by [18] that "heavy metals is a sum parameter in the form of Pb, equivalents of following heavy metals: As, B, Cr, Cu, Hg, Mn, Mo, Ni, Pb and Sb," and according to the estimations published by [61], as well as following the [62, 63] indication, that environmental parameters in LCA studies are independent and usually follow the lognormal distribution as do the impact results [59]. Other studies showed that the lognormal distribution has been used by [9] for the variability assessment by means of bootstrap technique (applied for the computation of the median absolute deviation (MAD) for measure of the *variability* in statistical analysis). As pointed out by [62], the lognormal distribution has an upside-down bathtub-shaped hazard rate [64, 65], and no negative values are possible [18]. Lognormal distribution always remains positive, and it is consistent with the data available in the ecoinvent database and the pedigree matrix approach, as suggested by [45]. In addition, it is interesting to note that according to analysis, the trace element concentrations in gold processing have been concluded that concentration distribution of the elements between the grinding stages and the discharge stages was not uniform probably due to the different physical and chemical processes at various stages [64, 65].


Several studies have presented examples of the utilization of MC simulation in LCA studies; however, according to [67], MC and fuzzy set theory have been applied in a limited number of LCA studies. According to [25] the LCA data, in general, is full of uncertain numbers, and these uncertainties, for instance, are caused by uncertain measurement or uncertainty about how representative a data is for the analyzed problem [25]. Bieda [23] depicted that the reliability of LCA results may be uncertain, to a certain degree, and this uncertainty can be pointed out using MC method. In order to obtain robust conclusions about LCA results, the uncertainty needs to be sufficiently accommodated [68], and in order to apply the MC approach, it is needed to translate own information about uncertainty into a standard distribution type [32]. In this study each REE is independent (uncorrelated) of the others and comes from the same source (i.e., laboratory). Uncorrelated means that deviations for all products (elements) are independent [45]. In carring out the MC simulation used CB (10,000 runs) obtained histograms, shown in **Figure 1**, statistics, as well as percentiles reports presented in **Tables 2** and **3**, respectively, are present the results obtained by MC simulation for the sum (total) of the Sc, Dy, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Ho, Er, Tm, Tb, Yb, and Lu. The confidence interval is 95%. This means that 95% of the results lay within this range [25]. Total forecast value amounted to the geometric mean value of the 56.59 ppm contained between 51.20 ppm and 62.58 ppm (see **Figure 2**). After 10,000 runs, the standard error of the mean is 0.04. The entire range which expressed the 95% confidence interval is from 45.78 ppm to 69.17 ppm. Range width is 23.38 ppm. The number displayed in the upper right corner of the histogram showed 9887 data points inside 2.6 SD of the mean [19, 20]. Just below the horizontal axis at the extremes of distribution, there are two small triangles, called endpoint grabbers [19, 20]. The certainty range (confidence interval) is displayed at the lower center of the frequency charts—the area of the histograms covered by them is darker [19, 20]. A detailed description of the simulation performed using CB is given in [19, 20, 23, 24]. The outcomes of the MC simulation listed in **Table 3** indicate that, for example,

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the chance that the total REEs will be less than 56.49 ppm is only 50% [19, 20].

The definition of sensitivity analysis (SA) given by [30] is "the study of how the uncertainty in the output of model (numerical or otherwise) can be apportioned to different sources of uncertainty in the model input." According to suggestion [45], SA isolates the main drivers of impact (and possibilities for improvement) and should be included in complete assessment of uncertainty. It is worth pointing out that Kolb [69] noted that theoretical methods are sufficiently advanced, so that it is intellectually dishonest to perform modeling without SA (see [30]). According to [70], SA of a result is most often studied parameter by parameter, while according to [71], SA helps decision-makers to understand the impact of chosen allocation

The result of this SA with the confidence level of 95%, created on the basis of SRCC and sorted in descending order, where positive correlation coefficients indicate that the acceptance of the stricter assumptions can be associated with obtaining the higher forecast probability [23, 24], for the data presented in **Table 1**, is shown in **Figure 3**. Positive coefficient signifies the existence of positive correlation, whereas the negative coefficient signifies negative correlation

**4.2. Sensitivity analysis**

method and boundary setting on LCA results.

μ<sup>g</sup> = geometric mean value; σ<sup>g</sup> = geometric standard deviation.

**Table 1.** Overview of the rare earths taken into account in the study (all values in ppm).

Finally, in this study to address uncertainty in the inventory data, analyzed REEs were fitted by lognormal distributions based on the real data summarized in **Table 1**. The CB lognormal distribution tab windows included the lognormal distributions of each of the 16 analyzed REEs after defining the geometric mean value (μ<sup>g</sup> ) automatically which calculated (matches) the standard deviation (σ<sup>g</sup> ) and lower as well as upper boundaries of lognormal distribution. There is lack of critical details in literature on how experimental data (e.g., σ<sup>g</sup> ) with regard to probability distributions for the REEs in monazite was calculated. Moreover, lack of expert knowledge and transparency makes it extremely difficult for other researches to carry out their studies [48]. As noted above, *monazite* is the second most important rare earth, after bastnaesite [48]. The results of the performed simulation (10,000 runs) can be presented in the form of frequency charts shown in **Figure 5**.

#### **4.1. Uncertainty analysis: MC simulation results**

The literature includes many studies and papers dealing with the uncertainty analysis. According to [66], the uncertainty analysis can vary from a qualitative assessment (where parameters are assigned a low, medium, or high level of uncertainty) to a semiquantitative assessment in which parameter values are bounded [66].

Several studies have presented examples of the utilization of MC simulation in LCA studies; however, according to [67], MC and fuzzy set theory have been applied in a limited number of LCA studies. According to [25] the LCA data, in general, is full of uncertain numbers, and these uncertainties, for instance, are caused by uncertain measurement or uncertainty about how representative a data is for the analyzed problem [25]. Bieda [23] depicted that the reliability of LCA results may be uncertain, to a certain degree, and this uncertainty can be pointed out using MC method. In order to obtain robust conclusions about LCA results, the uncertainty needs to be sufficiently accommodated [68], and in order to apply the MC approach, it is needed to translate own information about uncertainty into a standard distribution type [32].

In this study each REE is independent (uncorrelated) of the others and comes from the same source (i.e., laboratory). Uncorrelated means that deviations for all products (elements) are independent [45]. In carring out the MC simulation used CB (10,000 runs) obtained histograms, shown in **Figure 1**, statistics, as well as percentiles reports presented in **Tables 2** and **3**, respectively, are present the results obtained by MC simulation for the sum (total) of the Sc, Dy, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Ho, Er, Tm, Tb, Yb, and Lu. The confidence interval is 95%. This means that 95% of the results lay within this range [25]. Total forecast value amounted to the geometric mean value of the 56.59 ppm contained between 51.20 ppm and 62.58 ppm (see **Figure 2**). After 10,000 runs, the standard error of the mean is 0.04. The entire range which expressed the 95% confidence interval is from 45.78 ppm to 69.17 ppm. Range width is 23.38 ppm. The number displayed in the upper right corner of the histogram showed 9887 data points inside 2.6 SD of the mean [19, 20]. Just below the horizontal axis at the extremes of distribution, there are two small triangles, called endpoint grabbers [19, 20]. The certainty range (confidence interval) is displayed at the lower center of the frequency charts—the area of the histograms covered by them is darker [19, 20]. A detailed description of the simulation performed using CB is given in [19, 20, 23, 24]. The outcomes of the MC simulation listed in **Table 3** indicate that, for example, the chance that the total REEs will be less than 56.49 ppm is only 50% [19, 20].

#### **4.2. Sensitivity analysis**

Finally, in this study to address uncertainty in the inventory data, analyzed REEs were fitted by lognormal distributions based on the real data summarized in **Table 1**. The CB lognormal distribution tab windows included the lognormal distributions of each of the 16 analyzed

**REEs Distribution type Atomic number μg σ<sup>g</sup> Quality Reference** Scandium (Sc) Lognormal 21 0.41 1.10 0.41 CB® result Yttrium (Y) Lognormal 39 3.25 1.10 3.27 CB® result Lanthanum (La) Lognormal 57 12.13 1.10 12.19 CB® result Cerium (Ce) Lognormal 58 23.86 2.39 23.89 CB® result Praseodymium (Pr) Lognormal 59 2.39 1.10 2.4 CB® result Neodymium (Nd) Lognormal 60 9.78 1.10 9.83 CB® result Samarium (Sm) Lognormal 62 1.74 1.10 1.75 CB® result Europium (Eu) Lognormal 63 0.45 1.10 0.45 CB® result Gadolinium (Gd) Lognormal 64 1.27 1.10 1.28 CB® result Terbium (Tb) Lognormal 65 0.14 1.10 0.14 CB® result Dysprosium (Dy) Lognormal 66 0.49 1.10 0.49 CB® result Holmium (Ho) Lognormal 67 0.08 1.10 0.08 CB® result Erbium (Er) Lognormal 68 0.22 1.10 0.22 CB® result Thulium (Tm) Lognormal 69 0.03 1.10 0.03 CB® result Ytterbium (Yb) Lognormal 70 0.17 1.10 0.17 CB® result Lutetium (Lu) Lognormal 71 0.02 1.10 0.02 CB® result

probability distributions for the REEs in monazite was calculated. Moreover, lack of expert knowledge and transparency makes it extremely difficult for other researches to carry out their studies [48]. As noted above, *monazite* is the second most important rare earth, after bastnaesite [48]. The results of the performed simulation (10,000 runs) can be presented in the

The literature includes many studies and papers dealing with the uncertainty analysis. According to [66], the uncertainty analysis can vary from a qualitative assessment (where parameters are assigned a low, medium, or high level of uncertainty) to a semiquantitative

There is lack of critical details in literature on how experimental data (e.g., σ<sup>g</sup>

= geometric standard deviation.

**Table 1.** Overview of the rare earths taken into account in the study (all values in ppm).

) automatically which calculated (matches)

) with regard to

) and lower as well as upper boundaries of lognormal distribution.

REEs after defining the geometric mean value (μ<sup>g</sup>

form of frequency charts shown in **Figure 5**.

**4.1. Uncertainty analysis: MC simulation results**

assessment in which parameter values are bounded [66].

the standard deviation (σ<sup>g</sup>

μ<sup>g</sup> = geometric mean value; σ<sup>g</sup>

32 Lanthanides

The definition of sensitivity analysis (SA) given by [30] is "the study of how the uncertainty in the output of model (numerical or otherwise) can be apportioned to different sources of uncertainty in the model input." According to suggestion [45], SA isolates the main drivers of impact (and possibilities for improvement) and should be included in complete assessment of uncertainty. It is worth pointing out that Kolb [69] noted that theoretical methods are sufficiently advanced, so that it is intellectually dishonest to perform modeling without SA (see [30]). According to [70], SA of a result is most often studied parameter by parameter, while according to [71], SA helps decision-makers to understand the impact of chosen allocation method and boundary setting on LCA results.

The result of this SA with the confidence level of 95%, created on the basis of SRCC and sorted in descending order, where positive correlation coefficients indicate that the acceptance of the stricter assumptions can be associated with obtaining the higher forecast probability [23, 24], for the data presented in **Table 1**, is shown in **Figure 3**. Positive coefficient signifies the existence of positive correlation, whereas the negative coefficient signifies negative correlation

**Figure 1.** The frequency chart of the 16 analyzed REEs forecasted with 95% confidence level (source: own work).

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34 Lanthanides

**Figure 1.** The frequency chart of the 16 analyzed REEs forecasted with 95% confidence level (source: own work).

#### 36 Lanthanides


**Table 2.** Statistical report of outcomes from the simulation.


**Table 3.** Percentile report of outcomes from the simulation.

[23, 24], or in other words, positive coefficients indicate that an increase in the assumption is associated with an increase in the forecast; negative coefficients imply the reverse [19, 20]. The MC simulation results have then been used also to perform the SA, presented in the form of tornado charts (see **Figures 4** and **6**) and spider charts (see **Figures 5** and **7**). According to [72] the concentrate that contains a mix of phosphates (apatite and monazite) can be further enriched through magnetic separation thanks to the paramagnetic property of monazite (apatite is nonmagnetic). Magnetic separation leads to the production of a concentrate containing 17.5% of the initial phosphate content (monazite mainly) and the REE content from 170 ppm to 5,000 ppm for Ce (90 ppm to 2,800 ppm for La and 70 to 2,300 ppm for Nd).

The sensitivity analysis demonstrates that Ce, La, and Ne are the most sensitive parameters and will be used for further analysis. The tornado and spider charts have been created on the basis of data included in the newly built tables, **Tables 4**–**7**, respectively. Tornado chart and spider

**Figure 4.** Tornado sensitivity chart of the Ce, La, and Ne scenario based on the percentiles of the variables, testing range

of 10–90%. Error bars indicate mean standard errors (source: own work).

**Figure 2.** Frequency chart of the total REE forecast expression (95% confidence level), obtained from a MC simulation of

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10,000 runs. Certainty range is from 51.20 pm to 62.58 ppm (source: own work).

**Figure 3.** Sensitivity analysis with confidence levels of 95% (created by SRCC) (source: own work).

Life Cycle Inventory (LCI) Approach Used for Rare Earth Elements (REEs) from Monazite Material… http://dx.doi.org/10.5772/intechopen.80261 37

**Figure 2.** Frequency chart of the total REE forecast expression (95% confidence level), obtained from a MC simulation of 10,000 runs. Certainty range is from 51.20 pm to 62.58 ppm (source: own work).

**Figure 3.** Sensitivity analysis with confidence levels of 95% (created by SRCC) (source: own work).

[23, 24], or in other words, positive coefficients indicate that an increase in the assumption is associated with an increase in the forecast; negative coefficients imply the reverse [19, 20]. The MC simulation results have then been used also to perform the SA, presented in the form of tornado charts (see **Figures 4** and **6**) and spider charts (see **Figures 5** and **7**). According to [72] the concentrate that contains a mix of phosphates (apatite and monazite) can be further enriched through magnetic separation thanks to the paramagnetic property of monazite (apatite is nonmagnetic). Magnetic separation leads to the production of a concentrate containing 17.5% of the initial phosphate content (monazite mainly) and the REE content from 170 ppm

to 5,000 ppm for Ce (90 ppm to 2,800 ppm for La and 70 to 2,300 ppm for Nd).

**Percentile Total (ppm)** 0% 45.78 10% 53.00 20% 54.16 30% 55.01 40% 55.78 50% 56.49 60% 57.20 70% 58.02 80% 59.00 90% 60.34 100% 69.17

**Table 2.** Statistical report of outcomes from the simulation.

36 Lanthanides

**Statistics Total (ppm)** Trials 10,000 Mean 56.59 Median 56.49 Mode — Standard deviation 2.89 Variance 8.36 Skewness 0.21 Kurtosis 3.11 Coeff. of variability 0.05 Range maximum 45.78 Range minimum 69.17 Range width 23.38 Mean std. error 0.03

**Table 3.** Percentile report of outcomes from the simulation.

**Figure 4.** Tornado sensitivity chart of the Ce, La, and Ne scenario based on the percentiles of the variables, testing range of 10–90%. Error bars indicate mean standard errors (source: own work).

The sensitivity analysis demonstrates that Ce, La, and Ne are the most sensitive parameters and will be used for further analysis. The tornado and spider charts have been created on the basis of data included in the newly built tables, **Tables 4**–**7**, respectively. Tornado chart and spider

**Figure 5.** Spider sensitivity chart of the Ce, La, and Ne scenario based on the percentiles of the variables, testing range of 10–90%. Error bars indicate mean standard errors (source: own work).

**Figure 6.** Tornado sensitivity chart of the Ce, La, and Ne scenario based on the percentage deviation from the base case method, testing range from −10% to +10%, using existing cell values (source: own work).

chart of the Ce, La, and Ne median-value base case model for input testing ranging from 10 to 90% that used percentiles of the variables method were presented in **Figures 4** and **5**, while tornado chart and spider chart of the Ce, La, and Ne based on the existing cell-value base case model for input testing ranging from −10% to +90% that used percentage deviation from the base case method were presented in **Figures 6** and **7**, respectively. Red bar indicates that the value was produced by the downside (lower bound), and a blue bar indicates that the value was produced by the upside (upper bound). Error bars indicate mean standard errors. The importance of the examined REEs is illustrated by the length of the associated bar. The rest 13

**REE total sum Input**

**Table 4.** The MC simulation results, using CB for the tornado sensitivity analysis-sensitivity table.

**Table 5.** The MC simulation results, using CB for the spider sensitivity analysis-sensitivity table.

**Variable Downside Upside Range Downside Upside Base case** Ce 54.204 58.976 4.772 21.474 26.246 23.86 La 55.371 57.809 2.438 10.971 13.409 12.19 Nd 55.607 57.573 1.966 8.847 10.813 9.83

**Variable −10.0% −5.0% 0.0% 5.0% 10.0%** Ce 54.204 55.397 56.59 57.783 58.976 La 55.371 55.9805 56.59 57.1995 57.809 Nd 55.607 56.0985 56.59 57.0815 57.573

**Table 7.** The MC simulation results, using CB for the spider sensitivity analysis-sensitivity table.

**REE total sum Input**

**Table 6.** The MC simulation results, using CB for the tornado sensitivity analysis table.

**Variable 10.0% 30.0% 50.0% 70.0% 90.0%** Ce 53.51325061 55.15231499 56.36230629 57.63727651 59.59987966 La 54.90673258 55.74412549 56.36230629 57.01368462 58.01637248 Nd 55.18853356 55.8638061 56.36230629 56.88757692 57.6961431

**REE total sum**

**REE total sum**

**Variable Downside Upside Range Downside Upside Base case** Ce 53.51325061 59.59987966 6.086629053 20.89253168 26.97916073 23.74158736 La 54.90673258 58.01637248 3.109639906 10.67392964 13.78356954 12.12950335 Nd 55.18853356 57.6961431 2.507609539 8.60744285 11.11505239 9.78121558

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**Figure 7.** Spider sensitivity chart of the Ce, La, and Ne median value scenario based on the percentage deviation from the base case method, testing range from −10% to +10%, using existing cell values (source: own work).


**Table 4.** The MC simulation results, using CB for the tornado sensitivity analysis-sensitivity table.


**Table 5.** The MC simulation results, using CB for the spider sensitivity analysis-sensitivity table.


**Table 6.** The MC simulation results, using CB for the tornado sensitivity analysis table.

**Figure 6.** Tornado sensitivity chart of the Ce, La, and Ne scenario based on the percentage deviation from the base case

**Figure 7.** Spider sensitivity chart of the Ce, La, and Ne median value scenario based on the percentage deviation from the

base case method, testing range from −10% to +10%, using existing cell values (source: own work).

**Figure 5.** Spider sensitivity chart of the Ce, La, and Ne scenario based on the percentiles of the variables, testing range of

method, testing range from −10% to +10%, using existing cell values (source: own work).

10–90%. Error bars indicate mean standard errors (source: own work).

38 Lanthanides


**Table 7.** The MC simulation results, using CB for the spider sensitivity analysis-sensitivity table.

chart of the Ce, La, and Ne median-value base case model for input testing ranging from 10 to 90% that used percentiles of the variables method were presented in **Figures 4** and **5**, while tornado chart and spider chart of the Ce, La, and Ne based on the existing cell-value base case model for input testing ranging from −10% to +90% that used percentage deviation from the base case method were presented in **Figures 6** and **7**, respectively. Red bar indicates that the value was produced by the downside (lower bound), and a blue bar indicates that the value was produced by the upside (upper bound). Error bars indicate mean standard errors. The importance of the examined REEs is illustrated by the length of the associated bar. The rest 13 REEs were not included in the process of generating tornado and spider charts as other thirteen REEs are not in the field of ENVIRRE project research scope and interest.

**Acknowledgements**

**Funding**

**Author details**

**References**

2018-06-11]

10.1002/9781119275039.ch17

of Raw Materials in Europe 2014.

and Technology, Kraków, Poland.

Dariusz Sala\* and Bogusław Bieda

\*Address all correspondence to: dsala@zarz.agh.edu.pl

**Compliance with ethical standards**

The authors are grateful for the input data provided as part of the environmentally friendly and efficient methods for extraction of rare earth elements from secondary sources (ENVIREE) project funded by NCBR within the second ERA-NET ERA-MIN Joint Call Sustainable Supply

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This work was supported by the Management Department of the AGH University of Science

Management Department, AGH University of Science and Technology, Kraków, Poland

[1] Dias MIM, Borcia CG, Menard Y. Deliverable D1.2 report on the physical-chemical properties of available materials for the recovery of REE and Deliverable D1.3 chemical and mineralogical data of secondary REE sources (Dias et al. 2016). 2016. Available from: http://www.enviree.eu/fileadmin/user\_upload/ENVIREE\_D1.2\_and\_D1.3.pdf [Accessed:

[2] Vahidi E, Zhao F. Life cycle analysis for solvent extraction of rare earth elements from aqueous solutions. In: Proceedings in the Conference: Rewas 2016: Towards Materials Resource Sustainability: Towards Materials Resource Sustainability. DOI:

*Conflict of interest*: the authors declare that they have no conflict of interest.

Research is not involving human participants and/or animals.

Spider chart is obtained by perturbing Ce, La, and Nd median values (input variables) at consistent (testing) range from 10 to 90% from the base case, which used percentile of the variables from the base case method. The vertical y-axis maps the location measure of distribution expressed in percentages (percentile of the variables) ranging from 10 to 90% (see **Figure 6**). The variation of each input parameter (Ce, La, and Nd) (e.g., by 10, 50, and 90%) showed how much the output (REE Total sum) changes.

Spider chart is obtained by perturbing Ce, La, and Ne median values (input variables) at consistent (testing) range from 10 to 90% from the base case, which used percentile of the variables from the base case method. The vertical y-axis maps the location measure of distribution expressed in percentages (percentile of the variables) ranging from 10 to 90% (see **Figure 6**). The horizontal x-axis maps the sum of analyzed REEs (in ppm). As a result, the spider chart enables the possibility to simultaneously compare the examined REEs [23, 24].

## **5. Conclusions**

This study refers to uncertainty in the input parameters used to create LCI of REE recovery processes from secondary sources performed according to ISO 14040 (2006). The focus of this study is defined in the goal and scope and was developed using the primary and secondary data.

Due to uncertainty analysis, a final result is obtained in the form of value range. The results from this study suggest that MC simulation is an effective method for quantifying parameter uncertainty in LCA studies.

The analyzed parameters are assigned with lognormal distribution. It is concluded that uncertainty analysis offers a well-defined procedure for LCI studies; early phase of LCA as the deterministic analysis does not include uncertainty in the input data.

The methodological approach regarding databases and boundaries was transparent and fully documented. Moreover, the results of this study can help to assess environmental impacts of rare earth mining, because production of REEs is associated with considerable environmental burdens. Additionally these result inventory data will be available for LCIA and, finally, for full LCA analysis. The obtained results may be also useful and interesting for further studies of REE recovery and could be used to other domestic and international LCA studies, and the study results demonstrate the utility of the MC simulation for a clear interpretation of LCA results. Moreover, they can also help scientist gain a cleaner understanding of the stochastic modeling in the environmental engineering and could be useful tool for decision support methods such as multi-criteria decision analysis.

And finally, consideration of uncertainty in LCA provides additional scientific information for decision-making, as discussed in the work of Romero-Gámez et al. [73].
