Waste Classification of Spent Refractory Materials to Achieve Sustainable Development Goals Exploiting Multiple Criteria Decision Aiding Approach

Featured Application

The method presented in this paper can be applied in waste management for the achievement of sustainable development goals.

Abstract

The recycling of used refractory materials in the heavy industry constitutes one of the significant environmental problems in the industry related to environmental and financial issues. This study proposes a multicriteria methodological frame to characterize the refractory material waste and identify the recycling capabilities. Considering the chemical and physical analysis of the refractory material wastes, the proposed methodological frame progresses into a two-phase procedure. The first phase includes an on/off approach that allows discretizing the refractory material wastes to compatible or not compatible as far as their recycling prospects. Then, an additive value model is utilized, including (a) the marginal value functions used for every criterion related to critical environmental factors, and (b) the weight vector reflecting the relative importance of the criteria used. A group of experts concerning the environment and the refractory materials was employed to estimate the additive value model. The assessment of the marginal value function is achieved using the module of the Multicriteria Interactive Intelligence Decision Aiding System (MIIDAS), which is based on a modification of the mid-value split point technique incorporating focused dialogues, artificial intelligence, and visual techniques. The weight vector was assessed using the weight assessment through prioritization method (WAP), which concludes with the estimation of the weights based on the criteria ranking and the pairwise expression of the strength of preferences for the consecutive criteria according to their ranking. The outcome of this approach is to introduce an environmental appropriateness index for refractory materials based on their chemical composition and the judgement of an expert group. The main findings of this research may be useful for engineers, decision-makers, and scientists in the field of circular economy and waste management.

1. Introduction

Through applying alternative use cycles, the circular economy (CE) aims at reducing dependency on (new) natural resource extraction, while expanding the time that resources spent within the technology sphere [1]. In essence, this approach of CE imitates Earth’s naturally circular systems [1]. CE envisions a balance between industry and the environment, ensuring that human civilization will continue to thrive in the long run. All waste is designed to become reusable material through different processes. Following the example of the ecosystems, material cycles in CE are closed [1]. Many researchers have studied the different aspects raised by the two main pillars of CE, namely, the technical model [2,3,4,5,6,7] and the biological model [8,9,10]. Fereira et al. [2], Horckmans et al. [3], Fang et al. [4], Hanagiri et al. [5], Poirer et al. [6], and Ariannpour et al. [7] dealt with refractory characterization and recycling. Pantazopoulou et al. [8] and Kasina et al. [9] concluded on issues related to the stabilization and potential reuse of sewage sludge and municipal waste incineration ashes. Moreover, Vlachokostas et al. [10] suggested a framework supporting the decision making for biodegrabable waste management. On the other hand, Kyriakopoulos et al. [11] concluded that there are still many issues leading to the negative environmental impacts that arise from the fundamental assumptions of CE.

Environmental characterization is crucial throughout all stages of refractory material life as it assists in evaluating, mitigating, and controlling risks. Refractory solid materials are used in industries (steel, cement, aluminum, glass, ceramics, etc.) where there are requirements to withstand very high temperatures. Refractory materials are produced from abundant industrial minerals, including chromite, dolomite, SiO₂, MgO, and Al₂O₃ [2]. Refractories are the primary materials applied as the internal lining of kilns, incinerators, and furnaces. Because these materials are exposed to elevated temperatures and corrosive liquids or gases, they have to meet different challenging specifications, such as thermal expansion, mechanical strength, and corrosion resistance [2]. Refractories are produced in shape form (bricks) for lining subsystems of the industry or in powder form, which is shaped on the installation site.

Refractories are classified into acidic, basic, or neutral according to the interaction of water with the primary raw material. Acid refractories, including silica, zircon, and alumina silicates are typically applied for lower operating temperatures [3]. Basic refractories, such as doloma, spinel, and magnesia, are usually combined with graphite and carbon and applied in highly basic environments [3]. Neutral refractories, including alumina and chromia refractories, are applied broadly by the metal industries because of their moderate price, elevated melting temperature, and ability to be applied in basic and acidic environments [3,4].

The industries (metal, cement, glass, etc.) from time to time (depending on the type of production) replace the refractories into the frame of maintenance of the industrial units. It is estimated that, worldwide, 35–40 million tons of refractories are produced and used yearly, and an amount of about 28 million tons of spent refractories are produced [3]. Even in this vast amount of spent refractory material, it is worth mentioning that, in the last 20 years, the recycling processes have not seen a massive utilization since (a) the production cost of the raw material was low, and (b) the cost of disposal of the used refractories was not high.

Many of the abovementioned elements were changed recently, while many environmental issues were raised concerning the handling of the refractory wastes and the increased cost of landfilling. Furthermore, in the EU, new regulations and directives were posed concerning the environment, such as the waste frame Directive 2008/98/EC, which poses the priorities for handling the wastes, ordered as follows [12]: (a) prevention, (b) preparation for reuse, (c) recycling, (d) recovery, and (e) disposal. Even the increasing interests in the waste disposal of recycling spent refractories are a common approach worldwide for the management of spent refractories. Therefore, reuse and recycling become of higher importance and influence handling of the spent refractories.

The decision to reuse or recycle the refractory waste depends on a set of parameters, the most important of which are (a) the quality of the spent refractories, (b) the previous use of the refractories and the substances deposited on their surface, (c) the type of refractory, (d) the composition of refractory materials which could contain potentially toxic elements posing a threat to human and ecosystems, and (e) the leachability of potentially toxic elements from refractories.

Another significant parameter to be considered is the type of recycling process. The closed-loop process concerns the use of the spent refractories producing new refractories. This is the most attractive since the recycling of the spent refractories is focused on added-value products with high production cost as far as the required energy is concerned.

The interest in reusing refractory spent materials with better environmental characteristics is expected to grow in the upcoming years. Therefore, it is crucial to evaluate the ecotoxicological potential of the refractory spent materials. The evaluation of potential ecotoxicity of products/materials has been applied in several works [13,14]. The approach for evaluating the potential environmental risk of granular solid materials for ecotoxicological potential and landfilling was based on the Council Decision 2003/33/EC [15]. The appropriateness of the spent refractories for recycling is strongly dependent on the quality of the spent refractory and the clearness as far as the environmental impacts and health issues are concerned. The Council Decision 2003/33/EC discretized 15 components and their limits with respect to the content of the material used for which these can be characterized as inert, nonhazardous, and hazardous. In general, the proposed thresholds of concentration for the 15 components provide a guide for the acceptance for recycling of the wastes. A question is raised concerning the appropriateness of the spent refractories and the types of products of the recycling, and this decision is complicated related to (a) the kind of mineral of the refractory (chromite, dolomite, SiO₂, MgO, Al₂O₃, etc.), (b) the use of the recycling products in the industries whereby different qualities of refractories are used for different industries, and (c) the chemical and physical characteristics of the spent materials and, most importantly, their environmental appropriateness.

However, there is no commonly accepted approach in the literature that evaluates and quantifies the environmental appropriateness of waste materials by considering the concentration of the 15 components together with expert judgment. This study aims to fill this gap and is focused on the development of a methodological approach for (a) the discretization of the spent refractories to those that can be recycled, and (b) the development of a measure for the identification of the environmental appropriateness of the spent refractories which can be used for recycling. The measure is based on a structured multicriteria decision aid (MCDA) approach described later on, which will support decisions concerning the kind of recycling that can be used for any type of waste.

The paper is organized as follows: Section 1 includes the introduction which provides an overview of the current literature related to the specific topic. Section 2 provides a review of the management options for refractory spent materials, the main types of recycling, and the guidelines for the characterization of raw wastes based on the assessment of chemical toxicity. This section also includes an overview of MCDA methods and their applications in CE. Section 3 presents the proposed methodology for evaluating the appropriateness of recycling for refractory spent materials, while Section 4 describes the application of the proposed MCDA approach to spent refractories. Section 5 concludes the main findings of the study and proposes new avenues for future research.

2. Background

2.1. Refractory Spent Materials and Recycling

Landfilling is a standard management option for refractories, while the recycling process is an alternative one. The recycling of refractory spent material has emerged in the last few years. The main types of recycling are (a) open-loop and (b) closed-loop.

The main advantages of closed-loop recycling are the evolution toward CE and the potential to generate higher economic benefits. In closed-loop recycling, the intrinsic properties of the virgin material are not significantly different from those of the recycled material. Therefore, the recycled material can replace the virgin material and be applied in products as before. In open-loop recycling, the intrinsic properties of the virgin material differ from those of the recycled material. Therefore, the recycled material can replace other materials for other product applications [16].

The classical recycling process for refractory materials involves the following stages [5]: sorting and classification, crushing, sieving, and drying.

Currently, the majority of spent refractories are employed in low-grade applications such as roadbed construction or disposed of in landfills. Using the spent refractories for producing other types (open loop) of refractories is considered good practice but cannot be considered the best. The parameters controlling the recycling of refractories are, among others, the (a) economic cost of the virgin raw material, (b) type of usage, (c) composition of substances deposited on its surface, and (d) leachability of potentially toxic substances.

The studied refractory materials were used at high temperatures, particularly in metallurgical processes. According to Poirer et al. [6], refractories are not inert materials. In the aluminum and iron making processes at steelworks, various refractories are applied for the furnace linings for refining, smelting, and conveying operations. The degraded elements and impurities of refractories mainly include slag, base metal, and iron, while, technically speaking, eradicating such impurities is impossible [5]. Arianpour et al. [7] reported that about 70% of spent refractory bricks could be recycled successfully; while some refractories are reused as decoration in landscaping.

2.2. Characterization of the Spent Refractory Materials

The assessment of chemical toxicity of raw wastes, as well as of spent refractory materials, was conducted according to the standard leaching protocol EN 12457.04, which provides information on the mobility behavior of refractory materials of a particle size below 4 mm and applying a liquid to solid ratio of 10 L/Kg dry matter [17]. The characterization of the spent refractory materials is based on the Council Decision 2003/33/EC, regarding the acceptance of spent refractories at landfills [15]. The compliance of the testing results of the examined spent refractories with the Council Decision 2003/33/EC is a prerequisite in order for a spent refractory material to be accepted for dumping in a specific landfill [8]. Values of pH and concentration of arsenic (As), barium (Ba), cadmium (Cd), chromium total (Cr_total), copper (Cu), mercury (Hg), molybdenum (Mo), nickel (Ni), lead (Pb), antimony (Sb), selenium (Se), zinc (Zn), fluoride (F), chloride (Cl), and sulfate (SO₄²⁻) determined in the leachates of the spent refractory materials are compared against values given by Council Decision 2003/33/EC. According to this comparison, the spent refractory materials are classified as inert, non-hazardous, and hazardous (

Table 1. Leaching limit values established by Council Decision 2003/33/EC [15].

	Leaching Limit Values (L/S = 10 L/Kg)
Component	Inert	Non-Hazardous	Hazardous (Li)
pH	minimum 6
	mg/Kg
As	0.5	2	25
Ba	20	100	300
Cd	0.04	1	5
Crtotal	0.5	10	70
Cu	2	50	100
Hg	0.01	0.2	2
Mo	0.5	10	30
Ni	0.4	10	40
Pb	0.5	10	50
Sb	0.06	0.7	5
Se	0.1	0.5	7
Zn	4	50	200
F	10	150	500
Cl−	800	15,000	25,000
SO42−	1000	20,000	50,000

).

For the implementation of the proposed methodological approach, specific laboratory work and sample treatments have to be implemented.

The leachability of potentially hazardous substances from waste and spent refractory materials depends on the grain size distribution, solid-to-liquid ratio, mineral composition of the virgin material, content of amorphous components, and structure [9]. The As, Ba, Cd, Cr, Sb, Se, Hg, Mo, Ni, and Pb content of the leachates was obtained applying inductively plasma mass spectrometry (ICP-MS) and inductively coupled plasma optical emission spectrometry (ICP-OES). The Cu and Zn concentration of the leachate was determined using atomic absorption spectroscopy (AAS). Fluoride, Cl⁻, and SO₄²⁻ concentrations in leachates were measured applying titrating and gravimetric methods, respectively. X-ray diffraction (XRD) was applied for mineralogical characterization of spent refractory materials. As a complementary technique with XRD analysis, scanning electron microscopic (SEM) analysis was applied. In general, the mineralogical and chemical composition results are discussed to explain further the findings of the leachability tests and mobility of inorganic substances.

2.3. Multicriteria Decision Aid Methodologies and Circular Economy

According to Siskos and Spyridakos [18] and Pardalos et al. [19], MCDA procedures can be organized into four main theoretical trends: (a) value system approaches (analytic hierarchy/network processes—AHP/ANP [20,21,22], multi-attribute value/utility theory—MAVT/MAUT [23,24,25,26]), (b) outranking relations approaches [27,28,29,30,31], (c) disaggregation–aggregation approach [32,33,34], and (d) the multi-objective optimization approach [35,36,37,38].

Over the last decades, many studies [39,40,41] have been conducted to determine the most appropriate MCDA method for various research topics. These topics consider a wide variety of features, e.g., the type of the decision problem, the information required by the decision-maker, the dimensions of the performance table (i.e., number of criteria), the treatment of uncertainty, and the available robustness analysis techniques. Moreover, a decision support system was recently developed by Cinelli et al. [42] for recommending multicriteria decision analysis methods.

Many researchers have applied MCDA methods on issues related to CE [43,44,45,46,47,48,49,50]. According to Vlachokostas et al. [51], the AHP is mainly applied to real-life cases, while the MCDA approach is adopted to study issues related to incineration process, which present many similarities to the refractory material studied in the current research. More specifically, this study deals with the environmental appropriateness of the refractory materials which are involved, among others, in the incineration process.

3. Proposed Methodology for Appropriateness of Recycling

The proposed methodology for evaluating the appropriateness of recycling for refractory materials is a two-stage process. The first stage in an on/off process tests the refractory spent material in fulfilling the appropriateness for recycling. The second stage is based on a multicriteria methodological approach (MCDA) for the estimation of appropriateness for recycling on a scale of 0–1 [28,52]. The proposed MCDA methodology is mainly based on the estimation of additive value functions, which represent preferences of the decision making by assessing an overall score for each alternative [53,54]. The abovementioned index is further exploited to identify the use of the recycled refractories, considering the granulometric and mineral content. Three samples were received from the REFRACT project and nine virtual samples were used for the validation of the MCDA methodology.

3.1. The On/Off Criteria Process

The on/off criteria process is triggered by the chemical analysis implemented to representative samples of the spent refractories. The acceptance or not for recycling of the spent refractories is based on a set of rules related to the limits suggested by the Council Decision 2003/33/EC [15] concerning the metals and the undesirable substance (Table 1).

Figure 1 includes the steps for the proposed MCDA procedure according to the Council Decision 2003/33/EC.

The on/off criteria process examines the content of the refractory samples and the existence of a substance that exceeds the hazardous limits of Table 1, which can characterize the spent refractories as hazardous:

∃ i: T_di ≥ L_i the refractories are hazardous,

(1)

$$\forall \mathrm{i}:{ \mathrm{T}}_{\mathrm{di}}<{ \mathrm{L}}_{\mathrm{i}}, \mathrm{then} \mathrm{the} \mathrm{refractories} \mathrm{are} \mathrm{evaluated} \mathrm{for} \mathrm{environmental} \mathrm{appropriatenesss},$$

(2)

where d_i is component i, T_di represents the content of component d_i, and Li is the hazardous limit.

If all the component contents fall within the permissible limits for inert and nonhazardous substances, we can proceed to the next step to identify the degree of the appropriateness of the refractories for recycling (Figure 1). For example, a refractory sample with more than 70 mg·Kg⁻¹ Cr content but all the other components lower than the hazardous limits is characterized as hazardous and has to be secondarily examined as far as the granularity and the mineral content are concerned.

In cases where the component content falls within the permissible limits for the examined components, the MCDA approach is applied to identify the environmental appropriateness index (EAI).

3.2. Assessment of the Nonhazardous Spent Refractory Recycling Compatibility

The proposed multicriteria decision aid approach aims to assess the additive value model described below. Given a sample of refractory material d evaluated on n preference monotone or nonmonotone attributes G = {g₁,g₂, …, g_n}, a global value [32,52] is assigned through the utilization of the following formulae:

$$\mathrm{U}\left(\mathrm{d}\right)={\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{p}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}}\left(\mathrm{d}({\mathrm{g}}_{\mathrm{i}})\right), \mathrm{for} \mathrm{i}=1,2,..,\mathrm{n}{,}_{ }$$

(3)

$${\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{p}}_{\mathrm{i}}=1,{ \mathrm{p}}_{\mathrm{i}}\ge 0, \mathrm{for} \mathrm{i}=1,2,..,\mathrm{n},$$

(4)

where n is the number of attributes, d(g) = (d(g₁), …, d(g_n)) is the evaluation vector of the refractory material attributes, g_i* and g_i* are the least and most preferable levels of the attribute g_i, respectively, and u_i(g_i) and p_i are the value function and the relative weight of the i-th attribute; u(g_i*) = 0, u(g_i*) = 1.

For every pair of refractory material samples d_k and d_r, the additive value function satisfies the following conditions: (a) if U(d_k(g)) > U(d_r(g)), then d_k is more environmentally compatible than d_r; (b) if U(d_k(g)) = U(d_r(g)), then a_k has the same environmental compatibility as a_r.

The utilization of the marginal value functions supports the measurement of the relative impacts of every attribute, the importance of which concerns the environmental impacts.

3.2.1. Development of the Marginal Value Functions

The marginal value functions [52,55] denote the degree of environmental impacts of a factor d_i in the examined sample on a scale of 0–1, where 1 corresponds to totally inert materials and 0 corresponds to the level of concentration of hazardous materials (L_i). It is worth mentioning that the marginal value functions are usually not linear and can be upward, downward, concave, or s-shaped (Figure 2).

The curvature of the value function corresponds to the behavior of the factor as far as the environmental issues are concerned. A concave upward function means that significant environmental impacts are raised for low values of the attribute, while, in concave downward functions, only higher values of the attributes are significant for the environmental impacts. Siskos et al. [55] used a family of 12 general parametric forms f (a, b, c; g) to cover all types of monotone marginal value functions (concave, cave, and s-shaped general), as well as non-monotone attributes with ∪-shaped and ∩-shaped functions for the construction of the marginal values. There are two forms of marginal value functions: increasing preferences assigned to cases where the environmental impact is decreasing for higher values, and decreasing preferences where the environmental impact is increased for the higher values. In this study, the decreasing preference value functions are suitable for the parameters used, where a higher metal concentration leads to lower preferences as far as the environmental impacts are concerned. The exact estimation of the a, b, and c parameters of the value function is achieved utilizing a modified mid-value split point technique and dialogue with experts to conclude the appropriate value function for one of the attributes.

Actually, in this case, six consecutive ranges of the criterion range were used, and the experts ranked them according to their importance for changes from the lower value to the higher ones. In this way, the curvature of the marginal value functions was assessed, as well as the general form of the marginal value function. Then, utilizing the visual capabilities and artificial intelligence capabilities of the Multicriteria Interactive Intelligence Decision Aiding System (MIIDAS), the exact parameters of a, b, and c were calculated, and the precise form of the marginal value function was determined. Furthermore, interactive and visual processes can be used, where the shape of the value function is changed in controlled steps providing to the experts the marginal values to specific samples with known concentrations. In this way, experts are able to identify the function closer to their attitudes.

3.2.2. Weight Assessment

There are a large number of proposed methods in the literature for the estimation of criteria weights [56], such as AHP [22], the Simos technique [57,58,59], the MAUT compensatory technique [52], MACBETH (measuring attractiveness through a categorical-based evaluation technique) [60], and the weight assessment through prioritization (WAP) method [61].

In the proposed methodology, the weights of each attribute were assessed using the WAP method and the relative software developed to support the implementation of the method [61]. For every attribute a_i, a weight p_i is estimated. The method is proceeds in the following steps:

(a)

The experts rank order the attributes and the ex aequo sets of attributes in a pairwise manner, concerning their importance in environmental issues. The attributes are sorted according to their ranking from the most important to the least important and arranged in m classes (m ≤ n). Each class includes one attribute or a set of ex aequo criteria.

(b)

The key point of the WAP method is the utilization of the z indices for every pair of successive attributes or sets of ex aequo attributes that satisfy the following formula:

$$\frac{{\mathrm{p}}_{\mathrm{r}}}{{\mathrm{p}}_{\mathrm{r}+1}}={\mathrm{z}}_{\mathrm{r}}, \mathrm{for} \mathrm{r}=1, \dots , \mathrm{m}–-1,$$

(5)

where m is the number of importance classes for the criteria, z ≥ 1.

The WAP method does not require the precise identification of the z indices but a range [z_minr, z_maxr] where the value of z_r may vary. For two successive attributes or sets of ex aequo attributes (i.e., g_r, g_r+1), the range [z_minr, z_maxr] is identified such that z_minr ≤ z_r ≤ z_maxr. In order to facilitate the experts to identify this value system, visual interactive techniques are used. Through this approach, the DM is asked to sort the n attributes into m classes (m ≤ n) and to identify 2(m–− 1) values for the z_minr and z_maxr indices (r = 1, 2, …, m–− 1). Scroll bars are used to assist the visualization of the difference of the relative importance between two successive attributes or ex aequo sets of criteria, ordered by their ranking. The z_minr and z_maxr values are automatically calculated and presented with bars and unique labels.

Having identified the z_min and z_max for all the pairs of the successive classes, linear programming (LP) techniques are employed in order to estimate the minimum and maximum values of the weights. The following 2n optimization problem describes the estimation of the weight vectors for the maximization and minimization of the criteria weights:

Min p_i and Max p_i, for i = 1, 2, …, n,

(6)

subject to p_i–− p_i+1 = 0; if g_i+1 is followed by g_i and g_i+1 belongs to the same importance class r) as g_i or–p_i − p_i+1 * zmin_r ≥ 0,–p_i − p_i+1 * zmax_r ≤ 0; if g_i is followed by g_i+1, g_i belongs to the most important class (r) and g_i+1 belongs to class (r+1), p₁ + p₂ + … + p_n = 1, p₁ ≥ 0, p₂ ≥ 0, …, p_n ≥ 0.

Actually, the solutions emerging from the above LPs will lead to the identification of the minimum and maximum values of the criteria weights into the hyper-polyhedron (infinite solutions).

(c)

The robustness of the estimated hyper-polyhedron is calculated through the utilization of two indices. The first type of index used is the range between the maximum and minimum values of the criteria weights for every criterion, as these values are estimated for each vertex of the hyper-polyhedron. This gives a picture, at first glance, of the extent of robustness in each criterion. For instance, this index for the i-the attribute is calculated as follows:

$${\mathsf{\mu }}_{\mathrm{i}}=\left(\max \left({\mathrm{p}}_{\mathrm{ij}}\right)-\min \left({\mathrm{p}}_{\mathrm{ij}}\right)\right), \mathrm{forI}1,2,\dots ,\mathrm{n} \mathrm{I} \mathrm{j}=1,2,\dots ,\mathrm{m}{,}_{ }$$

(7)

where n is the number of attributes, m is the number of vertices of the hyper-polyhedron, and p_ij is the weight of the i attribute of the j vertex.

The second index used represents the normalized standard deviation of the different solutions corresponding to the hyper-polyhedron vertices, where the value 1 corresponds to the total robustness of the preferred models. This normalized index is called the average stability index (ASI) [62,63,64].

$$\mathrm{ASI}=1-\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}\sqrt{\left(\mathrm{m}\left({{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{m}}{\left({\mathrm{p}}_{\mathrm{i}}^{\mathrm{j}}\right)}^2\right)-{\left({{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{p}}_{\mathrm{i}}^{\mathrm{j}}\right)}^2\right)}}{\mathrm{m}\sqrt{\left(\mathrm{n}-1\right)}}{,}_{ }$$

(8)

where n is the number of attributes, and m is the number of vertices of the hyper-polyhedron.

Furthermore, for the set of 2n weight vectors, the barycenter is estimated. If the values of the barycenter are considered as satisfactory by the DM along with the level of robustness, then it can be used as a working vector of weights. Otherwise, there are two main capabilities provided by the proposed approach. The first focuses on updating or altering particular initial preferences, such as the values of the z_min and z_max or the criteria ranking. The second capability concerns the feedback with which the robustness can be analyzed, utilizing the tomographical approach [65] and eliciting additional preference information.

4. Results

4.1. Evaluation Model for Spent Refractories

The additive value model was assessed to fulfil the main objectives of REFRACT project. A further analysis was required concerning the appropriateness of the spent refractories for different types of recycling (open- or closed-loop).

Table 2. Samples (n = 12) of spent refractories, along with inert and hazardous limits.

Components	S2051	S2052	S2053	REF01	REF02	REF03	REF04	REF05	REF06	REF07	REF08	REF09	Inert	Non- Hazardous
As	0.050	0.050	0.050	0.400	0.200	0.270	1.000	0.700	1.900	22.000	13.000	19.000	0.5	2
Ba	0.500	0.500	0.500	17.000	7.000	9.000	80.000	71.000	22.000	278.000	101.000	144.000	20	100
Cd	0.002	0.002	0.002	0.020	0.010	0.030	0.700	0.180	0.310	3.000	2.000	3.000	0.04	1
Crtotal	0.500	0.500	0.500	0.100	0.250	0.400	4.000	0.600	0.600	11.000	55.000	61.000	0.5	10
Cu	1.000	1.000	1.000	0.200	0.160	0.170	26.000	2.100	39.000	100.000	55.000	77.000	2	50
Hg	0.010	0.010	0.010	0.001	0.007	0.002	0.140	0.070	0.160	0.330	0.570	0.900	0.01	0.2
Mo	0.500	0.500	0.500	0.050	0.010	0.400	2.000	9.000	0.700	29.000	17.000	22.000	0.5	10
Ni	0.040	0.040	0.040	0.140	0.110	0.270	3.000	3.000	7.000	14.000	39.000	11.000	0.4	10
Pb	0.500	0.500	0.500	0.050	0.340	0.300	5.000	0.610	8.000	38.000	11.000	48.000	0.5	10
Sb	0.050	0.050	0.050	0.010	0.020	0.050	0.210	0.440	0.570	0.800	3.900	0.800	0.06	0.7
Se	0.050	0.050	0.050	0.040	0.070	0.007	0.390	0.370	0.400	6.000	6.000	0.600	0.1	0.5
Zn	0.620	0.620	0.620	1.000	2.000	3.000	19.000	37.000	34.000	199.000	144.000	147.000	4	50
F	0.900	1.000	1.000	2.000	7.000	5.000	102.000	11.000	74.000	354.000	322.000	222.000	10	150
Cl−	71.000	71.000	71.000	457.000	91.000	770.000	4.000	1087.00	14,700.00	5.000	24,711.00	16,000.00	800	15,000
SO42−	148.000	123.000	288.000	222.000	124.000	7.000	11.000	14,777.00	5478.00	547.000	49,780.00	41,547.00	1000	20,000

tabulates the components content of the examined refractory samples used for the validation of the method. S2051, S2052, and S2053 were received from the REFRACT project, while REF01–REF09 were virtual samples.

4.1.1. Estimation of Marginal Value Functions Using the MIIDAS System

The experts utilized the techniques and visual capabilities of the MIIDAS system for the construction of the marginal value function [55]. For the components As, Cd, Cr, Sb, and Hg, upward concave functions were selected by the experts, whereby, for these components, lower concentrations were considered significant for environmental impacts. For the other attributes, downward concave functions were used since their impact was only considered significant for higher concentrations. Every marginal value function was refined through the process described above to identify the exact functions corresponding to every attribute.

Table 3. Marginal value functions for the 15 examined components—screen layouts of the MIIDAS system.

No.	Component	U = U (a, b, c; di)/[min, max] a, b, c Real	Marginal Value Function
1	As	$u\left(d\right)=a-b e^{c\left(1+\frac{9d}{25}\right)}, dϵ\left[0, 25\right]$ a = −0.0034999, b = −1.881829, c = −0.628751
2	Ba	$u\left(d\right)=a-b{e}^{c{\left(1+\frac{9d}{300}\right)}^{}}, dϵ\left[0, 300\right]$ a = −0.3045179, b = −1.533395, c = −0.161651
3	Cd	$u\left(d\right)=a-b{e}^{c{\left(1+\frac{9d}{5}\right)}^{}}, dϵ\left[0, 1\right]$ a = 0.5390968, b = −0.9881042, c = −0.7626 $u\left(d\right)=a+b{e}^{c{\left(1+\frac{9d}{5}\right)}^{}}, dϵ\left[1,5\right]$ a = 0.64202844, b = −0.009505888, c = 0.4210001
4	Crtotal	$u\left(d\right)=a-b e^{c\left(1+\frac{9d}{70}\right)}, dϵ [0,$ 70] a = −0.00727097, b = −1.742195, c = −0.547901
5	Cu	$u\left(d\right)=a-b{e}^{c{\left(1+\frac{9d}{100}\right)}^{}}, dϵ\left[0, 50\right]$ a = 0.5483023, b = −0.9684657, c = −0.7627 $u\left(d\right)=a+b{e}^{c{\left(1+\frac{9d}{100}\right)}^{}}, dϵ\left[50,100\right]$ a = 0.8111737, b = −0.05840966, c = 0.2631001
6	Hg	$u\left(d\right)=a-b{e}^{c{\left(1+\frac{9d}{2}\right)}^{}}, dϵ\left[0, 0.2\right]$ a = 0.5864021, b = −2.104839, c = −1.6271 $u\left(d\right)=a+b{e}^{c{\left(1+\frac{9d}{2}\right)}^{}}, dϵ\left[0.2, 2\right]$ a = 0.6454874, b = −0.009583134, c = 0.4210001
7	Mo	$u\left(d\right)=a-b{e}^{c{\left(1+\frac{9d}{30}\right)}^{}}, dϵ\left[0, 30\right]$ a = −0.2018096, b = −1.465328, c = −0.198251
8	Ni	$u\left(d\right)=a-b{e}^{c{\left(1+\frac{9d}{40}\right)}^{}}, dϵ\left[0, 40\right]$ a = −0.2032343, b = −1.466112, c = −0.197601
9	Pb	$u\left(d\right)=a-b{e}^{c{\left(1+\frac{9d}{50}\right)}^{}}, dϵ\left[0, 50\right]$ a = −0.08888087, b = −1.438429, c = −0.278401
10	Sb	$u=a-b{e}^{c\left(1+\frac{9d}{5}\right)}, dϵ [0,$ 5] a = −0.04104724, b = −1.491046, c = −0.359251
11	Se	$u\left(d\right)=a-b{e}^{c\left(1+\frac{9d}{7}\right)}, dϵ [0,$ 7] a = −0.0270333, b = −1.538527, c = −0.404151
12	Zn	$u\left(d\right)=a-b{e}^{c\left(1+\frac{9d}{200}\right)}, dϵ\left[0, 200\right]$ a = −0.2032343, b = −1.466112, c = −0.197601
13	F	$u\left(d\right)=a-b{e}^{c{\left(1+\frac{9d}{500}\right)}^{}}, dϵ\left[0, 500\right]$ a = −0.2242262, b = −1.478325, c = −0.188601
14	Cl−	$u\left(d\right)=a-b{e}^{c{\left(1+\frac{9d}{25,000}\right)}^{}},dϵ\left[0, 15,000\right]$ a = 0.562557, b = −0.8913583, c = −0.7118 $u\left(d\right)=a+b{e}^{c{\left(1+\frac{9d}{25,000}\right)}^{}},$ $dϵ\left[15,000, 25,000\right]$ a = 0.6260664, b = −0.001916413, c = 0.5789001
15	SO42−	$u\left(d\right)=a-b{e}^{c{\left(1+\frac{9d}{50,000}\right)}^{}},dϵ\left[0, 20,000\right]$ a = 0.4392703, b = −0.84213393, c = −0.4067 $u\left(d\right)=a+b{e}^{c{\left(1+\frac{9d}{50,000}\right)}^{}},$ $dϵ\left[20,000, 50,000\right]$, a = 0.6567029, b = −0.01649786, c = 0.3684001

includes the graphs of the marginal value function for the 15 attributes derived from the screen layout of the MIIDAS system used for the construction.

An example for developing the value function of As is demonstrated (Table 3). Since the leaching limit value for the inert class for As is 0.5 mg·Kg⁻¹ As, it is categorized in Group I. It is well known that As is a highly toxic element in its inorganic form and is widely recognized as carcinogenic, even at low concentrations [66,67]. The symptoms of As toxicity in humans include skin cancer, gangrene, leucomelanosis, keratosis, melanosis, and cancer of lungs, prostate and liver [66,67]. On the basis of the new scientific data correlated to the adverse health effects of As, the European Council and World Health Organization have established 10 μg As·L⁻¹ as the new parametric value for As in potable water, in contrast to the initial parametric value of 50 μg As·L⁻¹.

A hazardous material containing a content of As higher than the leaching limit value of 0.5 mg·Kg⁻¹ (Table 3) may release this element in the environment, contaminate groundwater, and pose a severe threat to human health. In this case, the slope of the proposed curve demonstrating the value function of As is high, suggesting that the value function of the MCDA approach for this element is rigorous considering the element’s toxicity.

4.1.2. Estimation of Criteria Weights Using the WAP Technique

Table 4. Components and their ranking applied in this study.

Component	Ranking
Cd	1
Hg	1
Sb	1
Se	1
As	2
Crtotal	2
Mo	2
Ni	2
Pb	2
Cu	3
Zn	3
Ba	4
F	4
Cl−	5
SO42−	5

provides the assessed ranking. There are various approaches suggesting criteria related to potential toxicity, human health, and ecological risk [66,67,68]. For the estimation of the criteria weights, the experts ranked the 15 elements and substances according to their potential toxicity. Through this process, five different ranking classes (1–5) were identified for chemical components, where 1 corresponds to high toxicity and 5 corresponds to low toxicity. The term “expert opinion” is used in contrast to “expert judgement” to emphasize an initial state of knowledge. The determination of expertise included professionals such as scientists and managers. Experts replied to the following research question: “What are the environmental quality expert’s views on the ranking of chemical components concerning their toxicity?” If the leaching limit value of a chemical component is 4, 3, 2, 1, and 0 orders of magnitude (rounded to the nearest power of 10) greater than the maximum leaching limit value for the inert category (1000 mg SO₄²⁻·L⁻¹), it belongs to Groups I, II, III, IV, and V, respectively. This classification is also in line with the parametric values for chemical components provided by the Council Directive 98/83/EC on the quality of water intended for human consumption [69].

The leaching limit values (L/S = 10 L/Kg) of chemical components for characterization as inert, non-hazardous, or hazardous waste were sorted in decreasing order and grouped in five classes as follows (Table 4): (a) Group I: Cd, Hg, Sb, Se; (b) Group II: As, Cr_total, Mo, Ni, Pb; (c) Group III: Cu, Zn; (d) Group IV: Ba, F; (e) Group V: Cl⁻, SO₄²⁻.

The next step of the methodology involved the relation of each group to a rank, as shown in Table 4.

Subsequently, the experts provided the relative importance (z_min and z_max) of the five classes utilizing the visual techniques of the WAP method and the relative software. Screen layouts are presented in Figure 3 for a comparison of the first and second classes (Figure 3).

Table 5. Estimation of weights.

Class/Order	Component	[Zmin, Zmax]	Pi	μi
1	Cd, Hg, Sb, Se	[1.3256, 1.5641]	0.1045	0.0186
2	As, Cr, Mo, Pb, Ni	[1.439, 1.667]	0.0725	0.0885
3	Cu, Zn	[1.299, 1.5]	0.0469	0.0094
4	Ba, F	[1.083, 1.2472]	0.03375	0.0105
5	Cl, SO42−		0.0292	0.0127
Average stability index (ASI)				0.989

presents the results of the relative importance provided by the experts, as well as the weights of the classes estimated by the linear program solution.

The above-presented methodological approach was utilized for the estimation characterization of the samples of spent refractories in the frame of the REFRACT project co-financed by the European Union and Greek national funds.

4.2. Classification of Refractory Spent Materials

The above additive value model was employed to estimate the environmental appropriateness index (EAI) for a set of samples with differentiations of the concentration of the components.

Table 6. Results of the EAI for the studied refractory samples and inert sample.

Weight	Components	S2051	S2052	S2053	REF01	REF02	REF03	REF04	REF05	REF06	REF07	REF08	REF09	Inert	Hazardous
0.07248	As	0.98871	0.98871	0.98871	0.91313	0.95558	0.94051	0.79673	0.85296	0.64924	0.00340	0.04942	0.01011	0.89262	0.63463
0.03375	Ba	0.99684	0.99684	0.99684	0.89677	0.95646	0.94429	0.58052	0.62000	0.86799	0.03429	0.49482	0.34437	0.87942	0.49871
0.10447	Cd	0.99874	0.99874	0.99874	0.98752	0.99372	0.98141	0.71542	0.89910	0.84026	0.49963	0.57436	0.49963	0.97538	0.65590
0.07248	Crtotal	0.96514	0.96514	0.96514	0.99293	0.98242	0.97201	0.75266	0.95831	0.95831	0.45683	0.01365	0.00644	0.96514	0.49071
0.04680	Cu	0.97003	0.97003	0.97003	0.99384	0.99507	0.99476	0.62412	0.93936	0.57936	0.00000	0.53169	0.34064	0.94206	0.56290
0.10447	Hg	0.97080	0.97080	0.97080	0.99698	0.97934	0.99399	0.73479	0.83414	0.71458	0.62332	0.60250	0.56516	0.97080	0.68203
0.07248	Mo	0.96479	0.96479	0.96479	0.99643	0.99929	0.97175	0.86522	0.50186	0.95099	0.01237	0.23544	0.12296	0.96479	0.46123
0.07248	Ni	0.99786	0.99786	0.99786	0.99253	0.99413	0.98564	0.84975	0.84975	0.67820	0.44246	0.00924	0.53459	0.97879	0.56813
0.07248	Pb	0.97306	0.97306	0.97306	0.99728	0.98160	0.98375	0.75866	0.96722	0.64036	0.03289	0.53857	0.00937	0.97306	0.57082
0.10447	Sb	0.96688	0.96688	0.96688	0.99329	0.98662	0.96688	0.86781	0.74221	0.67905	0.57954	0.04255	0.57954	0.96038	0.62099
0.10447	Se	0.97366	0.97366	0.97366	0.97887	0.96331	0.99627	0.81160	0.82036	0.80726	0.08420	0.01842	0.72491	0.94800	0.76501
0.04680	Zn	0.99338	0.99338	0.99338	0.98935	0.97879	0.96833	0.81296	0.66266	0.68607	0.00182	0.12240	0.12236	0.95796	0.56813
0.03375	F	0.99627	0.99585	0.99585	0.99172	0.97125	0.97940	0.64169	0.95513	0.72804	0.14385	0.18609	0.35195	0.95914	0.51149
0.02923	Cl−	0.99211	0.99211	0.99211	0.95166	0.98992	0.92167	0.99955	0.89365	0.55289	0.99944	0.03659	0.53012	0.91892	0.54817
0.02923	SO42−	0.99396	0.99497	0.98830	0.99096	0.99493	0.99971	0.99955	0.62936	0.81475	0.97799	0.00951	0.28179	0.96042	0.56896
	EAI	0.98009	0.98010	0.97991	0.98128	0.98138	0.97621	0.78548	0.81631	0.75179	0.31926	0.24560	0.36595	0.95464	0.60180

includes the results of the additive value model for the calculation of the environmental appropriateness index (EAI).

The EAI values for S2051, S2052, S2053, REF01, REF02, and REF03 samples were higher than the EAI value of the inert sample. The EAI value of the inert sample was estimated using the leaching limit values for the inert material (Table 6).

The component concentrations for samples S2051, S2052 and S2053 fell within the inert range (Table 2). Their EAI values were also higher than the corresponding inert limit for virtual samples REF01–REF03. The virtual samples (REF01–REF09) were used in order to validate the EAI, and the results can be considered satisfactory, since the EAI of samples REF04–REF06 varied between 0.75179 and 0.81631, which can be attributed to the concentrations exceeding the inert limit for most of the components (Table 2 and Table 6). Moreover, sample REF07 presented a low value of EAI (0.31926), attributed to the high content of the first-class components (Cd, Hg, Sb, Se), second-class components (As, Cr_total, Mo, Pb, Ni), third-class components (Cu, Zn), and fourth-class components (Ba, F) exceeding the upper nonhazardous limit. Furthermore, the lowest EAI value (0.2456) was observed for the REF08 sample which presented high concentrations of Ni, Sb, Se, Cl⁻, and SO₄²⁻, while REF09 (0.36595) presented high concentrations for all examined components (Table 2 and Table 6). Lastly, the above analysis reveals that the proposed index for measuring the appropriateness of the spent material can provide a rational measure for this case study.

5. Conclusions

This study introduced a multicriteria approach for the characterization of refractory material wastes concerning their recycling capabilities. For the above, a two-phase methodological approach was introduced. The first step of the proposed approach is to characterize the refractory material as inert or hazardous according to the composition of its leachate. Further analysis is performed in the second phase, where a multi-attribute index is introduced for the estimation of the environmental appropriateness of refractory spent materials. The critical features of the proposed methodological approach are (a) the utilization of a weight vector for the 15 critical substances, representing their relative importance related to the environmental impacts, and (b) a nonlinear value function encapsulating the variation of the environmental impacts on the scale of the acceptable concentration of the components in the refractory material waste.

The application of the proposed approach to a limited number of samples presented satisfactory results in measuring the environmental impacts of wastes that can be recycled. Engineers, decision-makers, and scientists may apply the proposed methodology by evaluating the different qualities of refractory material to specific parts of industrial systems since specific qualities of spent refractories can be used in several parts of kilns and furnaces exposed in various temperatures. This constitutes a new direction of this research and will be implemented in the next phase of the project, along with industrial experiments.

Lastly, the EAI value of a sample classified as nonhazardous may exceed the EAI value (0.95464) for inert limits. This corresponds to spent refractories with very good environmental appropriateness in terms of most components; thus, the application of further treatment should be investigated.

It is important to conduct further work on investigating the influence of uncertainties on the estimated parameters (e.g., the parameters of the nonlinear function) in the decision problem and to explore the suitability of other MCDA methods for this specific issue. The elicitation of the preference structure from other experts will be beneficial for the investigation of these parameters. The application of robustness analysis techniques, evaluating the preference structure and providing tools to improve it, will also be considered in future work.