Multi-objective optimization and performance evaluation of rotary furnace refractory linings using locally sourced materials

Abstract

This study optimizes refractory lining formulations for oil-fired rotary furnaces using locally sourced kaolin clay, processed into chamotte, and combined with raw kaolin, potter’s clay, and slaked lime. The Grey Taguchi method and grey relational analysis were employed to optimize cold crushing strength (CCS), thermal shock resistance (TSR), and open porosity (OP). Sixteen mixtures were prepared by varying material proportions, calcination temperature, and curing time. The optimal blend—70% chamotte, 28.5% raw kaolin, 6.5% pottery clay, and 1% slaked lime, calcined at 1350°C with 3 h of curing—demonstrated superior TSR and CCS while minimizing porosity. Confirmatory tests validated the formulation’s reliability, with results within a 95% confidence interval. ANOVA identified TSR as the most significant performance factor. The study highlights the effectiveness of combining Taguchi methods with grey relational analysis for multi-objective optimization, balancing competing performance metrics in refractory development. Industrial testing showed the optimized bricks withstanding over 30 furnace cycles, achieving a maximum service temperature of 750°C, and exhibiting improved energy efficiency (60%). These results demonstrate the potential of locally sourced materials to reduce reliance on imports and address challenges in the Ethiopian refractory industry. The findings contribute to sustainable, cost-effective refractory solutions for high-temperature industrial applications, promoting local production and resource utilization.

Keywords

refractory lining kaolin clay Grey Taguchi method thermal shock resistance cold crushing strength local materials multi-objective optimization

Introduction

Refractory linings are indispensable components in industrial furnaces, playing a pivotal role in ensuring operational efficiency, durability, and safety across industries such as metallurgy, ceramics, and petrochemicals. Composed of heat-resistant materials, these linings safeguard furnace walls from extreme temperatures, chemical corrosion, and mechanical wear, thereby extending furnace lifespan and minimizing energy losses. The selection and design of refractory materials are critical to optimizing furnace performance, reducing maintenance costs, and enhancing energy efficiency.¹

Oil-fired rotary furnaces, in particular, demand refractory linings with exceptional thermal shock resistance, high cold crushing strength, and low porosity to endure rapid temperature fluctuations and prolonged heating cycles. Suboptimal refractory materials can lead to frequent downtime, increased maintenance expenses, and energy inefficiencies due to heat leakage. As a result, there is a growing interest in cost-effective, locally sourced refractory materials, such as kaolin and potter’s clay, which not only reduce production costs but also diminish reliance on imported resources.^2,3

Recent advancements in refractory technology have focused on optimizing material formulations through advanced design techniques like Taguchi and grey relational analysis, which enhance multi-factor performance under varying operational conditions. Additionally, the global shift toward sustainable and economical production practices has underscored the importance of leveraging locally available resources, particularly in developing countries.^4–6 However, despite these advancements, a significant research gap remains in the systematic evaluation of locally sourced refractory materials for oil-fired rotary furnaces, particularly in terms of their long-term performance under extreme operational conditions. Furthermore, there is limited research on the integration of advanced optimization techniques with sustainable material sourcing to achieve a balance between cost-effectiveness and performance.

This study aims to address this gap by investigating the performance of locally sourced refractory materials, such as kaolin, firing condition effect using experiment and oil-fired rotary furnaces. By employing advanced optimization techniques and evaluating their thermal, mechanical, and chemical properties, this research seeks to contribute to the development of sustainable, cost-effective refractory solutions that meet the demanding requirements of modern industrial applications.

Literature review

Refractory materials are essential in high-temperature industrial processes, providing thermal insulation and structural integrity to furnaces, kilns, and reactors. They withstand extreme temperatures, mechanical abrasion, and chemical corrosion while maintaining stability. Classified into acidic, basic, and neutral categories, their performance depends on chemical composition and behavior under high temperatures.⁷ Common raw materials include kaolin, alumina, silica, and magnesite. Kaolin, when calcined to form chamotte, offers excellent thermal shock resistance (TSR) and mechanical strength. Recent studies highlight the role of mineralogical properties in enhancing refractory performance, with particle size distribution significantly impacting cold crushing strength (CCS) and porosity.^8–10

Recent advancements focus on optimizing refractory performance through advanced processing techniques. For example, basaltic tuffs have been explored as cost-effective raw materials.¹¹ Optimization frameworks like Taguchi and grey relational analysis enable fine-tuning of compositions for optimal mechanical properties and thermal resistance.¹² Similarly, studies on polymeric materials and composites emphasize the importance of optimizing cutting parameters for improved thermal management.¹³ Sustainability is a growing focus, with researchers utilizing locally sourced materials like kaolin and clay to reduce costs and environmental impact. Innovations in ceramic science and refractory engineering continue to enhance the durability and efficiency of furnace linings.^2,7

Refractory materials are indispensable in industries such as metallurgy, ceramics, glass manufacturing, cement production, and petrochemicals. They line furnaces, kilns, reactors, and incinerators, providing insulation, structural stability, and resistance to degradation. In the steel and iron industries, refractories are critical for blast furnaces, ladles, and converters, operating above 1500°C.¹⁴ In petrochemicals, they protect reactors from extreme heat and corrosive gases, with recent advancements improving thermal resistance, mechanical strength, and corrosion resistance.^7,15 Oil-fired rotary furnaces benefit from refractory linings designed to endure rapid thermal cycling. Locally sourced materials like kaolin and potter’s clay are increasingly used for cost efficiency and sustainability.^3,16

Thermal shock resistance (TSR) measures a material’s ability to withstand sudden temperature changes without cracking. Proper calcination of kaolin enhances TSR, as its mineral composition plays a critical role.¹⁷ Cold crushing strength (CCS) indicates a material’s mechanical strength under compression. Particle size and binder type significantly influence CCS, with optimization techniques like the Taguchi method improving performance.^18,19 Open porosity (OP) affects thermal conductivity and mechanical strength. Lower porosity enhances CCS and reduces heat loss, but an optimal balance is necessary to prevent brittleness.²⁰

Calcination transforms raw materials like kaolin into stable phases such as metakaolin and mullite. Optimal temperatures (600°C–1000°C) enhance CCS and TSR, but excessive heat can cause brittleness.²¹ Curing time ensures a stable microstructure, improving mechanical strength and durability. Longer curing times enhance CCS and reduce porosity, but must be balanced with production costs.^22,23

Kaolin, a clay mineral, is widely used in refractory production due to its abundance, plasticity, and heat resistance. When heated, kaolin transforms into metakaolin and mullite, enhancing mechanical strength and TSR.^24,25 Recent studies have optimized kaolin-based refractories by combining them with other materials. For example, smaller particle sizes improve CCS and TSR.²⁶ Advanced statistical methods like Taguchi and grey relational analysis enable researchers to balance TSR, CCS, and porosity.^27,28

In conclusion, refractory materials are vital for high-temperature industrial applications, with kaolin-based refractories offering a sustainable and cost-effective solution. Advances in material processing, optimization techniques, and sustainable sourcing continue to enhance their performance. By focusing on TSR, CCS, and porosity, and optimizing calcination and curing processes, researchers are developing more durable and efficient refractory materials for modern industrial needs.

Materials and methods

Materials

Commercial kaolin, a refined clay product, is widely recognized for its purity and consistent particle size distribution. It consists of hydrated aluminum silicate (Al₂Si₂O₅(OH)₄) with low impurities, characterized by high alumina content, contributing to its excellent refractory properties such as high-temperature resistance, low thermal conductivity, and minimal chemical reactivity. In this study, commercial kaolin serves as a standard reference material for comparing the performance of locally sourced alternatives.

The raw kaolin used in this research was mined from Debre Tabor, Ethiopia. It is a natural, unprocessed clay mineral primarily composed of kaolinite, along with quartz, feldspar, and other impurities. The chemical composition of raw kaolin influences its refractoriness and mechanical properties. Prior to use, the kaolin was fired to produce chamotte—a calcined form that enhances thermal stability and mechanical strength. The firing process, or calcination, involves heating the kaolin to 1350°C–1500°C to drive off chemically bound water, initiating the formation of the heat-resistant mullite phase.

Potter’s clay, also sourced from Debre Tabor, was used as a binder due to its high plasticity, which facilitates shaping and molding of refractory products. This clay consists of fine-grained minerals that offer excellent workability and cohesion. Its primary role in refractory formulation is to enhance mechanical bonding between chamotte and raw kaolin particles, contributing to improved cold crushing strength (CCS) and reduced porosity. The composition of potter’s clay includes alumina, silica, and trace impurities, which influence its performance in high-temperature applications. These locally sourced materials provide a sustainable and cost-effective solution for refractory production, reducing dependency on imported materials while harnessing Ethiopia’s natural resources.

Additives such as slaked lime and polyvinyl alcohol (PVA) were incorporated to optimize refractory properties. Slaked lime, added at 1%–2% by weight, acts as a mineralizer to enhance sintering and reduce porosity, while PVA (at ∼5% concentration) mitigates cracking during drying and improves mechanical integrity. These additives were selected based on their proven effectiveness in improving refractory performance.²⁹

Experimental design

This study utilizes chamotte, potter’s clay, kaolin, slaked lime percentages, calcination temperature, and curing time as controllable variables in developing the refractory lining formulation. A preliminary analysis, conducted using a one-variable-at-a-time approach, helped define the feasible range for these parameters. The selected parameters and their respective levels for experimentation are presented in Table 1, while Table 2 outlines the L16 orthogonal array used for designing the experiments. According to Taguchi’s design methodology, a mixed-level factorial design allows each parameter to be analyzed at mixed levels.^30,31 The degrees of freedom (DOF) for the parameters align with the requirements of an L16 (4 × 3 and 2 × 3) orthogonal array.³² Linear graphs guide the assignment of parameters within the array, ensuring an efficient and balanced experimental design.³³ This structured approach minimizes variation and enhances the reliability of the optimization process.

Table 1.

The control factors and their levels in refractory lining experiments.

Control factors	Levels
	1	2	3	4
Chamotte (%)	60	70	80	90
Pottery clay (%)	3.5	5	7	8
Raw kaolin (%)	14	20	28	32
Slaked lime (%)	1	2	0	0
Calcination temperature (°C)	1350	1450	—	—
Curing time (h)	2	3	—	—

Table 2.

The L16 orthogonal array layout for MINITAB.

Ex. no.	A	B	C	D	E	F
1	60	3.5	14	1	1350	2
2	60	5	20	1	1350	3
3	60	7	28	2	1450	2
4	60	8	32	2	1450	3
5	70	3.5	20	2	1450	2
6	70	5	14	2	1450	3
7	70	7	32	1	1350	2
8	70	8	28	1	1350	3
9	80	3.5	28	1	1450	3
10	80	5	32	1	1450	2
11	80	7	14	2	1350	3
12	80	8	20	2	1350	2
13	90	3.5	32	2	1350	3
14	90	5	28	2	1350	2
15	90	7	20	1	1450	3
16	90	8	14	1	1450	2

Experimental procedure

The experimental specimen preparation followed a systematic approach to ensure consistency and reliability as shown in Figures 1 and 2. The binder was prepared using a 4:1 volume ratio of potter’s clay and raw kaolin, a method aligned with modern practices for improving plasticity and workability in ceramic systems.³⁴ The mixture was homogenized using a sand muller and sieved through a 1000 µm mesh to ensure uniform particle distribution, critical for achieving optimal density and strength in the final product.³⁵

Figure 1.

Schematic representation of the experimental program for refractory specimen production.

Figure 2.

Specimen preparation setup: (a) sieve analyzer, (b) sieving mesh, (c) sand muller, and (d) press machine.

The transformation of kaolin into chamotte at 1500°C, followed by controlled cooling, aligns with contemporary thermal treatment strategies that promote the formation of mullite—a phase renowned for its excellent refractory properties.²⁴ Milling the chamotte to a particle size of 500 µm enhances its reactivity, contributing to improved mechanical strength, as finer particles facilitate better packing and reduced porosity.³⁴ The use of clay slip as a binder, derived from decanted slurry sieved to 100 µm, reflects current practices aimed at achieving uniform consistency and adequate plasticity.³⁶

Blending chamotte and raw kaolin in varied proportions, followed by compression in steel molds under 2 metric tons of pressure, adheres to standard refractory forming techniques designed to maximize green density and minimize defects.³⁴ The subsequent drying and firing at 1350°C for 2–3 h ensures proper sintering and the development of thermal stability, enhancing resistance to thermal shock and mechanical stress.^21,37 The gradual cooling process helps prevent cracking due to thermal gradients, maintaining the structural integrity of the refractory (Figure 3).³⁸

Figure 3.

Calcination of the samples in the furnace.

In our experiments, a programmable furnace with precise temperature control (±5°C) was employed to ensure uniform heating and cooling. The heating rate was maintained at 10°C per minute, allowing for gradual and consistent temperature increase.

During the heating phase, the refractory materials were subjected to controlled temperature increments, enabling the effective sintering and phase transformation processes. The target temperature was held for a specified duration to allow complete reaction and material stabilization.

In the cooling phase, the furnace was programmed to gradually reduce the temperature in a controlled environment, minimizing thermal gradients and internal stress development. This approach prevented cracks and structural defects, thereby preserving the material’s mechanical and thermal integrity.

Evaluation of refractory properties

The evaluation of refractory properties followed standard testing procedures to ensure accuracy and comparability with industrial benchmarks. Apparent porosity (AP), bulk density (BD), and water absorption tests were performed according to ASTM C20-00 specifications, critical for determining the material’s ability to resist penetration by molten materials and gases.³⁹ These properties directly influence thermal insulation performance and mechanical durability.⁷

Shrinkage (S), total shrinkage (TS), and loss-on-ignition (LOI) tests, carried out in line with ASTM C134-95, are vital for assessing dimensional stability and material composition after firing. Shrinkage impacts the dimensional accuracy of refractory bricks, while LOI provides insights into the amount of volatile materials driven off during firing, affecting the overall density and strength.³⁴

Cold crushing strength (CCS) was evaluated using ASTM C133-97, a key test for measuring the material’s resistance to compressive loads. High CCS indicates better mechanical performance under operational stresses.³⁴ Thermal shock resistance (TSR), determined using ASTM C1171-96, evaluates the material’s capacity to withstand rapid temperature fluctuations without cracking, a crucial property for oil-fired rotary furnaces.³⁷

Chemical composition analysis of the raw and processed materials was performed and compared with standard fireclay properties from literature. This comparison ensures that the materials meet the necessary chemical criteria for high-performance refractory applications.¹⁵

The refractoriness (R) of the samples was assessed using the Pyrometric Cone Equivalent (PCE) method, following ASTM C1525-18 guidelines. Sixteen sample mixtures were used to create custom pyrometric cones, adhering to the standard composition and specifications. These cones were positioned inside a furnace equipped with a thermocouple for precise temperature monitoring and subjected to elevated temperatures exceeding 1000°C to evaluate their performance under heat.

Statistical analysis and optimization framework

This study utilized the Taguchi method to optimize the proportions of chamotte, raw kaolin, slaked lime, potter’s clay, calcination temperature, and curing time, aiming to enhance key performance characteristics. By adopting an L16 orthogonal array, the experimental design efficiently reduced the number of required trials while maintaining the capacity to evaluate multiple factors simultaneously. Unlike a full factorial design, which would demand a more extensive experimental setup, this array allows for the analysis of up to six factors at four and two mixed levels with only 16 runs. This strategy demonstrates the practical advantages outlined by Krishnaiah and Shahabudeen,³¹ which highlighted the effectiveness of Taguchi’s designs in minimizing experimental effort without compromising analytical depth.

Taguchi’s methodology also facilitates the reduction of process variability and targets performance optimization using Signal-to-Noise (S/N) ratios, which balance the effects of control factors and response variability. The classification of S/N ratios into Nominal-the-Best (NB), Lower-the-Better (LB), and Higher-the-Better (HB), as explained by Krishnaiah and Shahabudeen,³¹ underscores their adaptability for different quality characteristics. This is estimated using equations (1)–(3).

Lower - the - better - 10 \log \frac{1}{n} \sum y^{2}

(1)

Higher - the better - 10 \log \frac{1}{n} \sum \frac{1}{y^{2}}

(2)

Nominal - the - best \frac{S}{N} = 10 \log \frac{y}{S_{y}^{2}}

(3)

Where n is the number of observations and y is the observed data.

Grey Relational Analysis (GRA) provides a systematic framework for evaluating relationships among system factors under uncertainty. By quantifying the degree of closeness between dynamic variables, GRA facilitates multi-criteria optimization. This approach has been widely recognized for its effectiveness in improving process stability and quality.⁴⁰

The first step in GRA involves normalizing raw data to ensure comparability across different performance metrics. Linear normalization techniques are commonly used to scale data within a standard range to mitigate dimensional inconsistencies.^33,41 In this study, key machining properties such as surface roughness and material removal rate were normalized using equations (4) and (5).

Larger-the-Better (Maximization):

\begin{matrix} {x^{*}}_{i} (k) = \frac{x_{i} (k) - min x_{i} (k)}{max x_{i} (k) - min x_{i} (k)}, i = 1, 2 \dots . ., m; \\ k = 1, 2 \dots \dots, n \end{matrix}

(4)

Smaller-the-Better (Minimization):

\begin{matrix} {x^{*}}_{i} (k) = \frac{max x_{i} (k) - x_{i} (k)}{max x_{i} (k) - min x_{i} (k)}, i = 1, 2 \dots . ., m; \\ k = 1, 2 \dots \dots, n \end{matrix}

(5)

Where m is the number of experiments, n is the number of response variables. Where x_i(k) is the original sequence of the response, $x_{i}^{*}$ (k) is the comparable sequence after data normalization, max x_i(k) and min x_i(k) are the largest value and smallest value of x_i(k) in this paper, m = 16, n = 8 is taken.

The quality loss function, denoted as Δ_oi(k), represents the absolute difference between the reference sequence $x_{o}^{*}$ (k) and the comparability sequence $x_{i}^{*}$ (k). It quantifies the deviation of each performance characteristic from the ideal target value, providing a measure of how closely a process variable aligns with the optimal condition. The quality loss function is mathematically defined as:

Δ_{oi} (k) = x_{o}^{*} (k) - x_{i}^{*} (k)

(6)

The Grey Relational Coefficient (GRC) is calculated to evaluate the relationship between the ideal reference sequence and each comparative sequence. GRC determines the relative closeness of a factor’s behavior to the desired performance. Recent studies⁴² emphasize that GRC provides a solid foundation for computing the Grey Relational Grade (GRG), integrating multiple performance characteristics into a single optimization metric.

The GRC is calculated using the following equation:

γ (x_{0}^{*} (k), x_{i}^{*} (k)) = \frac{Δ_{\min} + τ Δ_{\max}}{Δ_{oi} (k) + τ Δ_{\max}}

(7)

Where ζ is the distinguishing coefficient and ζ [0, 1]. ζ is set at 0.5.

Δ_{\min} = min_{\forall_{i}} 1 min_{\forall_{k}} Δ_{oi} (k)

Δ_{\max} = max_{\forall_{i}} 1 max_{\forall_{k}} Δ_{oi} (k)

γ(k) = Grey Relational Coefficient for the i-th alternative and k-th performance characteristic.

Δ_i(k) = Absolute difference between the reference sequence (y₀(k)) and the normalized value (y_i(k)):

Δ_min = Minimum value of Δ_i(k) across all alternatives and characteristics.

Δ_max = Maximum value of Δ_i(k) across all alternatives and characteristics.

In multi-objective optimization, assigning appropriate weights to performance characteristics is crucial. Principal Component Analysis (PCA) is widely used in Grey Relational Analysis (GRA) to improve accuracy and objectivity.⁴³ The process begins by computing correlation coefficients between performance characteristics to construct a correlation matrix. Eigenvalues and eigenvectors are then extracted, where eigenvalues represent the variance explained by each principal component. Eigenvectors provide a directional measure of influence for each performance characteristic. Only components with eigenvalues greater than 1 are considered significant.^44,45

The contribution ratio of each characteristic is obtained by squaring the elements of the eigenvector, revealing the relative significance of each factor. These ratios are then used as weight factors in GRA, ensuring that the weighting scheme is data-driven rather than subjective.⁴³

The correlation coefficient formula is given by:

C_{ke} = \frac{cov (x_{i}^{*} (j) x_{i}^{*} (k))}{σ x_{i} (j) σ x_{i} (k)}

(8)

Where j, k represent performance characteristics, $cov (x_{i}^{*} (j) x_{i}^{*} (k))$ is the covariance of sequence $x_{i}^{*} (j)$ ) and $x_{i}^{*} (k)$ , $σ x_{i} (j)$ and $σ x_{i} (k)$ are the standard deviations of sequence of $x_{i}^{*} (j)$ ) and $x_{i}^{*} (k)$ respectively.

The Grey Relational Grade (GRG) is a key metric for evaluating the correlation strength between the reference sequence and comparability sequence in multi-objective optimization. It integrates multiple performance measures into a single value. Studies by Wang et al.⁴³ suggest that GRG is best calculated as the weighted sum of Grey Relational Coefficients.

The GRG formula is given as:

Ψ (x_{o}^{*}, x_{i}^{*}) = \sum_{k = 1}^{n} ω_{k} γ (x_{o}^{*} (k), x_{i}^{*} (k))

(9)

Where Ψ is the weight of the kth performance characteristics and $ω_{k}$ denotes the weight assigned to the k-th performance characteristic, derived from PCA.

Results and discussion

Quality characteristics of the refractory samples

Experiments were conducted using an L16 orthogonal array, with results presented in Table 3. The signal-to-noise (SN) ratios, calculated using equations (1)–(3), are shown in Table 4. Lower SN ratios for fired shrinkage (FS) and total shrinkage (TS) indicate poorer performance, with Trial 6 showing the lowest FS SN ratio (−10.881) and Trial 8 the lowest TS SN ratio (−14.807). Conversely, higher SN ratios for bulk density (BD) and thermal shock resistance (TSR) signify better performance, with Trial 5 achieving the highest BD SN ratio (2.734) and Trial 8 the highest TSR SN ratio (63.227). Cold crushing strength (CCS) peaked in Trials 6 and 14 (7.197), while apparent porosity (AP) was lowest in Trials 2, 11, and 12 (−27.780, −27.651, −27.776). The SN ratio method effectively identifies optimal parameter levels for enhancing refractory properties.

Table 3.

The responses L16 orthogonal array.

Ex. no.	FS (%)	TS (%)	BD (g/cm³)	SG	TSH (cycles)	CCR (kN/cm²)	AP (%)	R (°C)
1	3.25	5.44	1.36	2.57	96.00	2.30	24.67	1470
2	3.33	5.44	1.36	2.58	92.90	2.30	24.49	1440
3	3.40	5.39	1.37	2.60	91.28	2.30	24.24	1420
4	3.39	5.40	1.37	2.59	91.62	2.30	24.27	1424
5	3.28	5.46	1.37	2.57	95.19	2.30	24.62	1459
6	3.50	5.24	1.36	2.64	88.11	2.29	23.51	1389
7	3.47	5.47	1.34	2.57	88.86	2.25	24.67	1397
8	3.50	5.50	1.33	2.56	88.11	2.23	24.80	1450
9	3.47	5.39	1.35	2.59	88.98	2.27	24.25	1397
10	3.47	5.39	1.35	2.59	88.98	2.27	24.25	1397
11	3.48	5.37	1.36	2.60	88.71	2.28	24.13	1396
12	3.42	5.44	1.35	2.57	90.41	2.29	24.48	1427
13	3.48	5.29	1.36	2.63	88.56	2.29	23.73	1393
14	3.47	5.48	1.34	2.57	88.81	2.25	24.68	1408
15	3.48	5.29	1.37	2.62	88.97	2.28	23.84	1397
16	3.47	5.34	1.37	2.61	88.97	2.30	23.97	1408

Table 4.

The SN ratio of L16 orthogonal array.

Ex. no.	FS (SN1)	TS (SN2)	BD (SN3)	SG (SN4)	TSH (SN5)	CCS (SN6)	AP (SN7)	R (SN8)
1	−10.238	−14.712	2.671	8.199	39.645	7.235	−27.843	63.346
2	−10.449	−14.712	2.671	8.232	39.360	7.235	−27.780	63.167
3	−10.630	−14.632	2.734	8.299	39.208	7.235	−27.691	63.046
4	−10.604	−14.648	2.734	8.266	39.240	7.235	−7.701	63.070
5	−10.318	−14.744	2.734	8.199	39.572	7.235	−27.826	63.281
6	−10.881	−14.387	2.671	8.432	38.901	7.197	−27.425	62.854
7	−10.807	−14.760	2.542	8.199	38.974	7.044	−27.843	62.904
8	−10.881	−14.807	2.477	8.165	38.901	6.966	−27.889	63.227
9	−10.807	−14.632	2.607	8.266	38.986	7.121	−27.694	62.904
10	−10.807	−14.632	2.607	8.266	38.986	7.121	−27.694	62.904
11	−10.832	−14.600	2.671	8.299	38.960	7.159	−27.651	62.898
12	−10.681	−14.712	2.607	8.199	39.124	7.197	−27.776	63.089
13	−10.832	−14.469	2.671	8.399	38.945	7.197	−27.506	62.879
14	−10.807	−14.776	2.542	8.199	38.969	7.044	−27.847	62.972
15	−10.832	−14.469	2.734	8.366	38.985	7.159	−27.546	62.904
16	−10.807	−14.551	2.734	8.333	38.985	7.235	−27.593	62.972

Table 5 presents normalized performance measures for key properties, including FS, TS, BD, SG, TSR, CCS, AP, and refractoriness (R). Experiment 8 consistently achieved the highest normalized values (close to 1.000), indicating superior performance across all parameters. In contrast, Experiments 6 and 16 showed lower values in specific gravity (SG), TSR, and CCS, suggesting suboptimal performance. Experiment 2 recorded the lowest AP (0.8820), indicating improved insulation. These findings highlight the importance of balancing mechanical strength, shrinkage control, and thermal resistance in refractory formulations.

Table 5.

Sequence after data preprocessing.

Ex. no.	FS	TS	BD	SG	TSH	CCS	AP	R
1	0.5101	0.8759	0.8478	0.9554	0.5293	0.7934	0.9500	0.5121
2	0.6825	0.8895	0.8293	0.8896	0.7094	0.7929	0.8820	0.6865
3	0.8056	0.7857	0.7958	0.7857	0.8056	0.7958	0.7857	0.8058
4	0.7857	0.8151	0.7958	0.8056	0.7857	0.7958	0.7958	0.7857
5	0.5773	0.9323	0.7967	0.9324	0.5756	0.7967	0.9321	0.5756
6	1.0000	0.4984	0.8330	0.4984	1.0000	0.8330	0.4984	1.0000
7	0.9505	0.9505	0.9487	0.9505	0.9535	0.9481	0.9499	0.9487
8	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.6321
9	0.9456	0.7905	0.8775	0.7905	0.9456	0.8775	0.7905	0.9456
10	0.9456	0.7905	0.8775	0.7905	0.9456	0.8775	0.7905	0.9456
11	0.9624	0.7424	0.8590	0.7424	0.9624	0.8639	0.7424	0.9565
12	0.8584	0.8764	0.9051	0.9456	0.8584	0.8248	0.8764	0.7639
13	0.9720	0.5842	0.8298	0.5842	0.9720	0.8298	0.5842	0.9703
14	0.9503	0.9544	0.9583	0.9550	0.9563	0.9525	0.9550	0.8824
15	0.9686	0.5912	0.7862	0.6292	0.9462	0.8577	0.6292	0.9462
16	0.9463	0.6909	0.7908	0.6803	0.9463	0.7908	0.6803	0.8827

Table 6 details the quality loss function (Δ_oi) values, with lower values indicating better conformity to desired properties. Trial 8 exhibited minimal quality loss across most parameters, except for R (0.3679), makes it the most optimal formulation. Conversely, Trial 6 showed the highest quality loss in TS and SG (0.5016), indicating significant deviations. Trials 7 and 14 achieved minimal quality loss in BD and AP, highlighting superior mechanical strength and insulation. This analysis underscores the importance of optimizing formulations to balance key properties.

Table 6.

Quality loss function.

Ex. no.	Δ_oi (FS)	Δ_oi (TS)	Δ_oi (BD)	Δ_oi (SG)	Δ_oi (TSR)	Δ_oi (CCS)	Δ_oi (AP)	Δ_oi (R)
1	0.4899	0.1241	0.1522	0.0446	0.4707	0.2066	0.0500	0.4879
2	0.3175	0.1105	0.1707	0.1104	0.2906	0.2071	0.1180	0.3135
3	0.1944	0.2143	0.2042	0.2143	0.1944	0.2042	0.2143	0.1942
4	0.2143	0.1849	0.2042	0.1944	0.2143	0.2042	0.2042	0.2143
5	0.4227	0.0677	0.2033	0.0676	0.4244	0.2033	0.0679	0.4244
6	0.0000	0.5016	0.1670	0.5016	0.0000	0.1670	0.5016	0.0000
7	0.0495	0.0495	0.0513	0.0495	0.0465	0.0519	0.0501	0.0513
8	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.3679
9	0.0544	0.2095	0.1225	0.2095	0.0544	0.1225	0.2095	0.0544
10	0.0544	0.2095	0.1225	0.2095	0.0544	0.1225	0.2095	0.0544
11	0.0376	0.2576	0.1410	0.2576	0.0376	0.1361	0.2576	0.0435
12	0.1416	0.1236	0.0949	0.0544	0.1416	0.1752	0.1236	0.2361
13	0.0280	0.4158	0.1702	0.4158	0.0280	0.1702	0.4158	0.0297
14	0.0497	0.0456	0.0417	0.0450	0.0437	0.0475	0.0450	0.1176
15	0.0314	0.4088	0.2138	0.3708	0.0538	0.1423	0.3708	0.0538
16	0.0537	0.3091	0.2092	0.3197	0.0537	0.2092	0.3197	0.1173

Table 7 presents grey relational coefficients (GRC), with higher values indicating better alignment with ideal properties. Trial 8 achieved the highest GRC (1.000) across all parameters, confirming its superior performance. Trials 7 and 14 also performed well, while Trial 6 recorded the lowest GRC values (0.4992), indicating poor thermal performance. This analysis supports the selection of formulations that balance mechanical strength, density, and thermal resistance.

Table 7.

Grey relational coefficients for 16 comparability sequence.

Ex. no.	FS	TS	BD	SG	TSH	CCR	AP	R
1	0.5051	0.8011	0.7666	0.9181	0.5151	0.7076	0.9091	0.5061
2	0.6116	0.819	0.7455	0.8191	0.6324	0.7071	0.8091	0.6146
3	0.72	0.7	0.71	0.7	0.72	0.71	0.7	0.7203
4	0.7	0.73	0.71	0.72	0.7	0.71	0.71	0.7
5	0.5419	0.8807	0.7109	0.8809	0.5409	0.7109	0.8804	0.5409
6	1	0.4992	0.7496	0.4992	1	0.7496	0.4992	1
7	0.91	0.91	0.907	0.91	0.9149	0.906	0.909	0.907
8	1	1	1	1	1	1	1	0.5761
9	0.9018	0.7047	0.8032	0.7047	0.9018	0.8032	0.7047	0.9018
10	0.9018	0.7047	0.8032	0.7047	0.9018	0.8032	0.7047	0.9018
11	0.93	0.66	0.78	0.66	0.93	0.786	0.66	0.92
12	0.7793	0.8018	0.8405	0.9018	0.7793	0.7405	0.8018	0.6793
13	0.947	0.546	0.746	0.546	0.947	0.746	0.546	0.944
14	0.9096	0.9165	0.923	0.9175	0.9196	0.9133	0.9175	0.8096
15	0.9409	0.5502	0.7005	0.5742	0.9029	0.7785	0.5742	0.9029
16	0.903	0.618	0.705	0.61	0.903	0.705	0.61	0.81

Principal Component Analysis (PCA) results in Table 8 reveal that Principal Component 1 (PC1) captures the most variance (eigenvalue: 4.3099), with significant contributions from FS, TS, CCS, and AP. PC2 (eigenvalue: 3.5067) emphasizes CCS and R, highlighting their role in mechanical strength and thermal response. PC3 and lower components contribute minimally. Sensitivity analysis in Table 9 shows that emphasizing PC1 increases the importance of parameters like SG and AP, while emphasizing PC2 elevates CCS and BD. This underscores the need for careful weighting in PCA-based studies.

Table 8.

Eigen values and Eigen vectors.

Principals	Variables								Eigen value
Principals	FS	TS	BD	SG	TSR	CCS	AP	R	Eigen value
PC1	0.35	−0.443	−0.206	−0.461	0.298	−0.104	−0.458	0.343	4.3099
PC2	−0.358	−0.19	−0.47	−0.146	−0.415	−0.511	−0.16	−0.367	3.5067
PC3	−0.259	0.206	−0.593	−0.264	−0.145	0.57	0.148	0.317	0.0932
PC4	0.455	0.608	−0.447	0.051	0.325	−0.225	−0.018	−0.254	0.0441
PC5	−0.362	0.487	0.208	−0.139	0.022	−0.464	−0.15	0.576	0.0239
PC6	0.575	0.048	−0.006	0.102	−0.735	−0.098	0.075	0.317	0.0113
PC7	−0.091	−0.283	−0.376	0.741	0.21	−0.166	0.086	0.378	0.0068
PC8	0.072	−0.189	−0.031	−0.341	0.164	−0.316	0.841	0.092	0.0041

Table 9.

Sensitivity analysis scenarios.

Parameters	Base scenario contribution	Scenario 1 contribution	Scenario 2 contribution	GRC	Base scenario GRG	Scenario 1 difference	Scenario 2 difference
FS	0.1227	0.1265	0.1242	0.869	0.1067	−0.0032	−0.0013
TS	0.1055	0.0841	0.1482	1.000	0.1055	0.0213	−0.0427
BD	0.1376	0.1674	0.0960	0.969	0.1333	−0.0288	0.0403
SG	0.1046	0.0787	0.1552	1.000	0.1046	0.0260	−0.0505
TSR	0.1317	0.1472	0.1138	0.999	0.1316	−0.0155	0.0179
CCS	0.1454	0.1860	0.0859	0.999	0.1453	−0.0406	0.0594
AP	0.1057	0.0808	0.1545	1.000	0.1057	0.0249	−0.0488
R	0.1241	0.1296	0.1228	0.919	0.1141	−0.0050	0.0013
GRG	0.9467	0.9677	0.9712		0.9467	−0.0210	−0.0245

This study employed Principal Component Analysis (PCA) to evaluate parameter contributions to dataset variance. Eigenvalues determined principal component importance, with results showing insensitivity to minor weighting changes. PC1 and PC2 accounted for 53.87% and 43.83% of variance, respectively, capturing 97.71% collectively. Squared loadings quantified parameter contributions within each component. As shown in Figure 4, Sensitivity analysis assessed three scenarios: a base scenario reflecting original variance distribution (PC1: 53.87%, PC2: 43.83%), Scenario 1 emphasizing PC1 (70% weight), and Scenario 2 emphasizing PC2 (70% weight). In Scenario 1, parameters with high PC1 loadings (e.g. SG, AP, TS) showed increased contributions, while those with high PC2 loadings (e.g. CCS, BD) decreased. Conversely, Scenario 2 elevated contributions of PC2-driven parameters (e.g. CCS, BD, and TSR) and reduced those of PC1-driven parameters. The base scenario provided a balanced benchmark. Sensitivity graphs (Grey Relational Grade, GRG) visually depicted these variations, highlighting the impact of component weighting on parameter importance. The analysis demonstrated that weighting choices significantly influence parameter contributions, emphasizing the need for careful consideration in PCA-based studies to ensure accurate interpretation and decision-making.

Figure 4.

Sensitivity graph for grey relational grade.

Table 10 highlights the contributions of individual parameters to combined PCs, with CCS (0.145407) and BD (0.137599) being the most influential. TSR and FS also contribute significantly, while TS has the lowest impact. This guides optimization efforts toward enhancing CCS, BD, and TSR for improved performance.

Table 10.

Contribution of response variables for the combined principal components.

Response variables	Contributions
FS	0.122734
TS	0.105463
BD	0.137599
SG	0.104631
TSR	0.1317
CCS	0.145407
AP	0.10573
R	0.124123

Table 11 presents grey relational grades (GRG) and S/N ratios, with Experiment 8 achieving the highest GRG (0.946736) and S/N ratio (−0.47542), identifying it as the optimal formulation. Experiment 16 ranked lowest (GRG: 0.723308), indicating significant room for improvement. This multi-objective optimization approach facilitates the development of robust refractory materials.

Table 11.

Grey relational grades for 16 comparability sequence.

Ex. no.	Overall grey relational grade	S/N
1	0.67769	−3.37938
2	0.697657	−3.12716
3	0.694609	−3.1652
4	0.693314	−3.1814
5	0.684208	−3.29624
6	0.748357	−2.51783
7	0.888594	−1.02593
8	0.946736	−0.47542
9	0.791253	−2.03369
10	0.791253	−2.03369
11	0.780877	−2.14835
12	0.769613	−2.27455
13	0.741683	−2.59564
14	0.882706	−1.08368
15	0.734865	−2.67585
16	0.723308	−2.81353

Figures 5 and 6 illustrate the effects of process parameters on GRG, with chamotte content (70%), pottery clay (7.0%), raw kaolin (28%), slaked lime (1%), curing temperature (1350°C), and curing time (3 h) identified as optimal settings. These findings demonstrate the effectiveness of grey relational analysis combined with Taguchi methods in optimizing refractory materials.

Figure 5.

Effects of process parameters on overall grey relational grade.

Figure 6.

Effects of process parameters on overall grey relational grade for SN ratio.

Figure 7 compares macro structural appearances of samples from Experiments 8, 12, and 1. Experiment 8 exhibited a smooth surface with minimal defects, while Experiment 1 showed roughness and cracks, confirming the correlation between GRG and material quality.

Figure 7.

Comparison of three experimental runs results: (a) experiment 8, (b) experiment 12, and (c) experiment 1.

Figure 8 presents residual plots for GRG, confirming the model’s statistical validity. The normal probability plot, residuals versus fitted values, histogram, and residuals versus order plots all support the model’s adequacy.

Figure 8.

Residual plots for grey relational grade.

Table 12 ranks factors by their influence on GRG, with chamotte (delta: 0.1262) and raw kaolin (delta: 0.1072) having the most significant impact. Curing time (delta: 0.0028) had the least influence, highlighting the importance of chamotte and kaolin in optimizing performance.

Table 12.

Response table for grey relational grade (response table for means).

Level	Chamotte	Pottery clay	Raw kaolin	Slaked lime	Calcination temperature	Curing time
1	0.6908	0.7237	0.7326	0.7814	0.7982	0.7640
2	0.8170	0.7800	0.7216	0.7494	0.7326	0.7668
3	0.7832	0.7747	0.8288
4	0.7706	0.7832	0.7787
Delta (max−min)	0.1262	0.0595	0.1072	0.0320	0.0655	0.0028
Rank	1	4	2	5	3	6

ANOVA results in Table 13 confirm the significance of chamotte (p-value: 0.025), raw kaolin (p-value: 0.032), and calcination temperature (p-value: 0.017) in determining GRG. Pottery clay, slaked lime, and curing time were less influential. The R-squared value (97.66%) indicates a robust model, reinforcing the critical role of chamotte, raw kaolin, and calcination temperature in optimizing refractory materials.

Table 13.

Result of ANOVA on grey relational grade (analysis of variance for grey relational grade).

Source	DF	Seq SS	Adj SS	Adj MS	F	p
Chamotte	3	0.0342737	0.0342737	0.0114246	15.27	0.025
Pottery clay	3	0.0094267	0.0094267	0.0031422	4.20	0.135
Raw kaolin	3	0.0287933	0.0287933	0.0095978	12.82	0.032
Slaked lime	1	0.0040957	0.0040957	0.0040957	5.47	0.101
Calcination temperature	1	0.0171865	0.0171865	0.0171865	22.97	0.017
Curing time	1	0.0000324	0.0000324	0.0000324	0.04	0.847
Error	3	0.0022451	0.0022451	0.0007484
Total	15	0.0960535

S = 0.0273563 R-Sq = 97.66% R-Sq(adj) = 88.31%.

In conclusion, this study demonstrates the effectiveness of SN ratio, grey relational analysis, and PCA in optimizing refractory formulations. Experiment 8 emerged as the most promising formulation, while Experiments 6 and 16 require further refinement. These findings provide valuable insights for developing high-performance refractory materials for demanding industrial applications.

Predicting optimal value

The optimal grey relational grade (µGRG) is predicted at the selected optimal setting of process parameters. The significant parameters with optimal levels are already selected as: A2, C3, and E1. The estimated mean of the response characteristic is computed as.³¹

μ_{GRG} = {\bar{T}}_{GRG} + ({\bar{A}}_{1} - {\bar{T}}_{GRG}) + ({\bar{C}}_{2} - {\bar{T}}_{GRG}) + ({\bar{E}}_{1} - {\bar{T}}_{GRG})

(10)

Where ${\bar{T}}_{GRG}$ = overall mean of grey relational grade = 0.782289. A2, C3, and E1 are the mean values of grey relational grade with parameters at optimum levels. From Figure 6, ${\bar{A}}_{2}$ = −1.829, ${\bar{C}}_{3}$ = −1.689, and ${\bar{E}}_{1} = - 2.014$ , Hence μ_GRG = 8.59368. A confidence interval for the predicted mean on a confirmation run is calculated using the equation (10).³¹

C I_{CE} = \sqrt{F_{α} (1, f_{e}) V_{e} [\frac{1}{n_{eff}} + \frac{1}{R}]}

(11)

Where: $F_{α}$ ; $F_{α} (1, f_{e})$ = F0.05;(1,3) = 10.13 (tabulated)

α = risk = 0.05,

f _e = error DOF = 3 (Table 13)

N = total number of experiments = 16

V _e = error variance = 0.0007484 (Table 13)

Total DOF associated with the mean (µGRG) = 15−3 = 12,

Total trial = 18, N = 18

n _eff = effective number of replications = N/{1 +[Total DOF associated in the estimate of mean]} = 18/(1 + 12) = 1.38

R = number of repetitions for confirmation experiment = 3

A confidence interval for the predicted mean on a confirmation run is ±0.098

The 95% confidence interval of the predicted optimal grey relational grade is: [µGRG − CI] < µGRG <[µGRG + CI] that is, 8.495 < µGRG < 8.692

Predicting value for multiple performance characteristics at optimal setting of process parameters are confirmed through experimental results as shown in Table 14.

Table 14.

Predicted and confirmation experimental values at optimal setting.

Performance characteristics	Optimal combination	Predicted grey relational grade	Predicted mean	Experimental value
Performance characteristics	Optimal combination	Predicted grey relational grade	Predicted mean	Exp1	Exp2	Exp3	Average
FS	A2B2C3D1E1F2	8.5937	−10.70237475	−10.6344	−10.7924	−10.6474	−10.6914
TS			−14.64006494	−14.5821	−14.7291	−14.5631	−14.6247
BD			3.636471491	3.684471	3.608471	3.546471	3.613138
SG			8.519084852	8.557085	8.489085	8.431085	8.492418
TSR			39.43673542	39.46474	39.48674	39.46974	39.47374
CCR			6.578648138	6.656648	6.644648	6.499848	6.600381
AP			−27.70687534	−27.6189	−27.6579	−28.6069	−27.9612
R			62.77834731	62.86835	62.86635	62.11835	62.61768

Confirmation test

As shown in Table 14, Confirmation experiments were conducted at the optimal levels (A2, B2, C3, D1, E1, and F2) identified through grey relational analysis. The predicted grey relational grade for this combination was 8.5937, with performance characteristics showing close alignment between predicted and experimental values. For fired shrinkage (FS), the experimental value (−10.691) slightly improved over the predicted value (−10.702). Total shrinkage (TS) also showed minimal deviation, with an experimental value of −14.624 compared to the predicted −14.64. Bulk density (BD) exhibited no significant variation, with experimental (3.613) and predicted (3.636) values closely matching. Specific gravity (SG) remained within the expected range at 8.49.

Thermal shock resistance (TSR) and cold crushing strength (CCR) demonstrated improved performance, with experimental values of 39.473 and 6.6, respectively, closely aligning with predictions (39.436 and 6.578). Apparent porosity (AP) showed a reduction (−27.961 experimental vs −27.707 predicted), enhancing material durability. Refractoriness (R) confirmed high thermal resistance, with an experimental value of 62.61 compared to the predicted 62.778. The grey relational grade at optimal levels (8.5937) confirmed significant performance improvement, falling within the 95% confidence interval of the predicted optimum condition.

Table 14 highlights the enhanced grey relational grade, validating the effectiveness of the optimization approach. These results demonstrate that grey relational analysis is a robust technique for optimizing multi-response problems in refractory material development, enabling significant improvements in material properties for industrial applications.

Chemical composition analysis: Comparative data

The chemical composition of raw kaolin clay, processed chamotte, optimized local refractory mixture, and commercial kaolin was analyzed to assess their suitability for refractory applications. Table 15 compares the major oxides (SiO₂, Al₂O₃, Fe₂O₃, K₂O, CaO, MgO, Cr₂O₃, Na₂O, TiO₂, and P₂O₅) and loss on ignition (LOI). The optimized refractory mixture exhibited the highest SiO₂ content (55.6 wt. %), followed by raw kaolin (54.2 wt. %), chamotte (52 wt. %), and commercial kaolin (49.4 wt. %). High SiO₂ enhances thermal stability but requires balanced Al₂O₃ for mechanical strength.^2,3 Commercial kaolin had the highest Al₂O₃ (33.4 wt. %), exceeding raw kaolin (23.8 wt. %), chamotte (25 wt. %), and the optimized refractory mixture (25.6 wt. %), highlighting its superior durability.⁷

Table 15.

Comparison of chemical composition (wt. %) of raw kaolin and processed chamotte mixture and optimized refractory mixture.

Oxides	Raw kaolin (wt. %)	Chamotte (wt. %)	Optimized refractory mixture (wt. %)	Commercial kaolin (wt. %)
SiO₂	54.2	52	55.6	49.4
Al₂O₃	23.8	25	25.6	33.4
Fe₂O₃	3.4	3	3.5	1.6
K₂O	3.87	3	3.3	1
CaO	0.69	0.5	1.5	0.3
MgO	0.23	0.5	0.5	0.3
Cr₂O₃	0	0	0	0
Na₂O	2.85	2	2.35	0.2
TiO₂	0.82	1	1.05	1.8
P₂O₅	0	0	0	0
LOI	9.47	9.6	10.7	12

Iron oxide (Fe₂O₃) levels were slightly higher in raw kaolin (3.4 wt. %) and the optimized refractory mixture (3.5 wt. %) compared to chamotte (3 wt. %) and commercial kaolin (1.6 wt. %). Elevated Fe₂O₃ can reduce thermal stability, making lower levels preferable.²¹ Alkali oxides (K₂O, Na₂O) were highest in raw kaolin (3.87 wt. % K₂O, 2.85 wt. % Na₂O) and lowest in commercial kaolin (1 wt. % K₂O, 0.2 wt. % Na₂O), aligning with industry standards for high-performance refractories, as alkali oxides act as fluxing agents, lowering melting points.⁷

The optimized refractory mixture showed the highest CaO content (1.5 wt. %), while MgO levels were comparable in chamotte and the optimized refractory mixture (0.5 wt. %). These oxides influence thermal stability and slag resistance, critical for furnace linings.³ Commercial kaolin contained the highest TiO₂ (1.8 wt. %), affecting color and thermal properties.⁷ LOI was highest in commercial kaolin (12 wt. %), followed by the optimized refractory mixture (10.7 wt. %), chamotte (9.6 wt. %), and raw kaolin (9.47 wt. %), indicating hydrated phases and impurities that may require additional processing.³⁵

The locally sourced refractory mixture aligns with ISO 10081 standards for low-alumina refractory bricks. While its higher Fe₂O₃ and alkali content may pose challenges, its overall composition is suitable for low-temperature aluminum melting furnaces.¹⁴

Performance evaluation in the industrial environment

The refractory brick industry in Ethiopia faces significant challenges due to limited domestic production and heavy reliance on imported fire clay. To address this, laboratory-optimized refractory bricks were developed and tested in an actual furnace environment. The results, presented in Table 16 and Figure 9, demonstrate their feasibility for industrial applications, offering a viable alternative to commercially available products. A comparative analysis against industry standards highlights their potential to enhance local production and reduce import dependency.

Table 16.

Test results of optimized refractory bricks and bricks lining in an actual furnace environment.

Properties	Result	Standard/requirement
compression strength (kN/cm²)	2.2	2–7
Water absorption (%)	4.58	4.5
Linear shrinkage (%)	3.1	7–9
Porosity (%)	13.32	10–15
Bulk density (g/cm³)	1.4	1.98
Refractoriness (°C)	1405	1400
Thermal conductivity coefficient (W/(m K))	1.1	0.01–1.1
Furnace cycle performance (cycles)	30+	30–60
Maximum service temperature (°C)	750	700–800
Energy efficiency (%)	60	50–70

Figure 9.

The oil fired furnace during testing in industrial set up at Bahir Dar textile factory.

The compressive strength of the optimized bricks was measured at 22 MPa, within the commercially acceptable range of 20–70 MPa, indicating sufficient mechanical strength for industrial furnaces.⁷ Water absorption was 4.58%, closely matching the commercial reference of 4.5%, suggesting comparable moisture management properties. Linear shrinkage was significantly reduced to 3.10%, compared to the conventional range of 7%–9%, enhancing dimensional stability and durability. Porosity was 13.32%, within the acceptable range of 10%–15%, contributing to both mechanical strength and thermal insulation. Bulk density was 1.4 g/cm³, lower than the 1.98 g/cm³ of commercial bricks, reflecting variations in raw material composition or processing methods but not compromising performance.

Refractoriness reached 1450°C, exceeding the typical commercial value of 1400°C, underscoring enhanced thermal stability. Thermal conductivity was 1.1 W/m K, aligning with the upper range of 0.01–1.1 W/m K for commercial counterparts, indicating effective heat management. The aluminum melting furnace of optimized bricks endured over 30+ furnace cycles, confirming their suitability for industrial applications. The maximum service temperature reached 750°C, aligning with the typical industrial requirement of 700°C–800°C for aluminum melting. Enhanced energy efficiency (60%) due to improved thermal properties further validates their effectiveness in high-temperature settings.

The optimized refractory bricks exhibit excellent performance in an aluminum melting furnace environment, with 30+ furnace cycles, a maximum service temperature of 750°C, and improved energy efficiency. These results confirm their suitability for industrial applications, particularly in aluminum melting, where thermal stability, durability, and energy efficiency are critical. This development addresses the challenges of the Ethiopian refractory industry, promoting local production and reducing dependency on imported materials. Further testing and scaling up of production are recommended to fully realize their potential in industrial settings.

In our study, the trade-offs between improved density and reduced cold crushing strength arises from the complex interaction between material composition and processing conditions. To balance these trade-offs, several strategies are proposed. First, optimizing the material composition by adjusting the ratio of chamotte, raw kaolin, and slaked lime can enhance microstructural bonding and control porosity. Incorporating micro or nano-sized reinforcements, such as alumina or silica nanoparticles, can improve strength without compromising density.

Second, utilizing Grey Relational Analysis (GRA) with Principal Component Analysis (PCA) allows for multi-objective optimization. By employing PCA-based weighting in GRA, appropriate importance can be assigned to each performance metric, reducing the dominance of a single property and achieving a more balanced optimization across multiple characteristics. Third, advanced sintering techniques, such as controlled calcination temperatures and optimized curing times, can enhance the material’s crystalline structure and reduce internal stresses. Exploring techniques like microwave sintering or hot isostatic pressing can further refine material properties. Fourth, the incorporation of additives and surface modifications can also be beneficial. Using binders and plasticizers during molding improves particle packing, while applying surface coatings or impregnation treatments enhances mechanical strength without significantly affecting density. Finally, leveraging machine learning models for iterative testing allows for the prediction and fine-tuning of process parameters based on experimental data. This approach helps identify optimal settings that balance competing performance metrics. These strategies collectively aim to mitigate inherent trade-offs and enhance the overall performance of the material.

Conclusion

This study successfully developed an optimized refractory lining formulation for oil-fired rotary furnaces using locally sourced materials, specifically kaolin clay, processed into chamotte, and combined with raw kaolin, potter’s clay, and slaked lime. By employing the Grey Taguchi method and grey relational analysis, the research optimized multiple performance metrics, including cold crushing strength (CCS), thermal shock resistance (TSR), and open porosity (OP). The optimal refractory blend was identified as 70% chamotte, 28.5% raw kaolin, 6.5% pottery clay, and 1% slaked lime, calcined at 1350°C with a curing time of 3 h. This formulation demonstrated superior thermal shock resistance and mechanical strength while minimizing porosity.

The experimental results, validated through confirmatory tests, confirmed the reliability and repeatability of the optimized formulation. Analysis of variance (ANOVA) highlighted that thermal shock resistance was the most significant factor affecting refractory performance. The study also demonstrated the effectiveness of combining Taguchi methods with grey relational analysis for multi-objective optimization, providing a robust framework for balancing competing performance metrics in refractory material development.

Furthermore, the chemical composition analysis of the optimized refractory mixture aligned with industry standards, making it suitable for industrial applications, particularly in aluminum melting furnaces. The optimized bricks exhibited excellent performance in industrial testing, withstanding over 30+ furnace cycles and achieving a maximum service temperature of 750°C. This performance coupled with improved energy efficiency and reduced reliance on imported materials, underscores the potential of locally sourced refractory materials to address the challenges faced by the Ethiopian refractory industry.

In conclusion, this research contributes to the development of sustainable, cost-effective refractory solutions for high-temperature industrial applications. The findings provide valuable insights for optimizing refractory formulations using locally available materials, promoting local production, and reducing dependency on imported resources. Future work should focus on scaling up production and further refining the material properties for broader industrial applications.

Footnotes

Handling Editor: Chenhui Liang

ORCID iD

Aragaw Mulu Muhaba

Funding

The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was partially funded by the Bahir Dar University (BDU), Bahir Dar Institute of Technology (BIT) through a school of research and graduate studies grant BDU/BIT/SRGS/138/2007.

Declaration of conflicting interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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