MATHEMATICAL PROCESSING OF RESULTS AND JUSTIFICATION OF OPTIMAL PARAMETERS FOR COAL BRIQUETTES PRODUCED FROM DISTILLERY VINASSE AND PARAFFIN WASTE

ABSTRACT

This study examines the production of coal briquettes from distillery vinasse and paraffin waste using a screw press unit. To justify the process settings, experimental design (mathematical planning) was employed, modeling factor effects on response criteria with a full second-order polynomial. Trials followed the V4 plan, and data processing with the Hartley–4 software yielded adequate regression equations. The optimal parameters were established as follows: binder fraction — 12%, seed-shell fraction — 24%, mixing/conditioning temperature — 96 °C, screw axial pressing force — 2.5 kN, and nozzle (die) diameter — 25 mm. Under these conditions, the briquettes exhibit compressive strength σ = 0.78 kg cm⁻², burning time τ = 110 s, and ash content of 11%. These results demonstrate that the selected feedstock blend and pressing regime enable briquettes with consistent performance suitable for practical use.

АННОТАЦИЯ

В работе исследовано получение угольных брикетов на основе спиртовой барды и парафиновых отходов с использованием шнекового пресс-агрегата. Для обоснования параметров процесса применено математическое планирование эксперимента; влияние факторов на критерии оценки аппроксимировано полным квадратичным полиномом. Эксперименты выполнены по плану В4, обработка данных и получение адекватных регрессионных уравнений проведены в программе «Хартли–4». Определены оптимальные технологические параметры: доля связующего — 12 %, доля скорлупы косточек — 24 %, температура термообработки при смешении — 96 °С, осевое усилие шнека — 2,5 кН, диаметр мундштука — 25 мм. При указанных условиях прочность брикетов составляет σ = 0,78 кг/см², время горения τ = 110 с, зольность — 11 %. Результаты подтверждают пригодность выбранной сырьевой композиции и режима прессования для получения брикетов с требуемыми эксплуатационными свойствами.

Keywords: Hartley–4; V4 design; distillery vinasse; paraffin waste; model; strength; nozzle (die); ash content.

Ключевые слова: Хартли–4; план (В4); спиртовая барда; парафиновые отходы; модель; прочность; мундштук; зольность.

Introduction. Based on multifactor experiments, the method of design of experiments (DOE) was employed to determine the optimal values of the recommended screw-press unit and the binder fraction. Briquetting of coal fines in the screw press and optimization of the resulting briquette parameters were carried out using an aqueous solution of a mixture of paraffin waste and distillery vinasse selected as the binder; to substantiate the optimal parameters of briquette porosity (with the aim of increasing porosity), both soft and hard seed shells were used as pore-forming agents.

Materials and methods. Theoretical studies and multifactor experiments identified the following variables as the most influential factors affecting briquette strength, burning time, and the amount of ash generated during combustion: binder fraction (X₁), seed-shell fraction (X₂), processing temperature during mixing (X₃), and the axial compaction force of the screw in the press (X₄) [1,2,3,4,5]. Based on the above theoretical and experimental results, the variation ranges of these factors were established. The factor levels and ranges are presented in Table 1.

Table 1.

Factor levels and change intervals

In the multifactor experiments, the response criteria were defined as briquette compressive strength (Y₁), burning time (Y₂), and ash content generated during combustion (Y₃). Assuming that the effects of the factors on the responses can be adequately described by a full second-order polynomial, the experiments were conducted according to the Hartley–4 design [4; 7; 8]. To reduce the influence of uncontrolled factors, the run order was randomized using the 1/17 scheme of the random-number table. For randomized combinations of factor settings, the observed ranges of Y₁, Y₂, and Y₃ were established; the computed values for these parameters are presented in Tables 2, 3, and 4, respectively.

Results. The experimental observations were averaged to obtain the arithmetic mean values for each run. Assuming that factor effects on the responses can be represented by a full second-order polynomial, the study employed the Hartley–4 design [6; 10; 13; 14]. The resulting mean responses were used to fit full quadratic models for briquette strength (Y₁), burning time (Y₂), and ash content (Y₃); these models form the basis for interpreting factor effects and determining optimal settings. The averaged data and model coefficients are summarized in the accompanying tables (see Tables 2–4).

Table 2.

Results of an experiment on the dependence of briquette durability on variable factors

Table 3.

The results of an experiment on the dependence of briquette burning time on variable factors

Table 4.

Results of an experiment on the dependence of briquette durability on variable factors

The experimental data were processed in accordance with standard procedures. Using the PLANEX package (Hartley–4 module), we obtained the following regression equations (1)–(3) that adequately describe the effects of the independent variables—binder fraction (X₁), seed-shell fraction (X₂), processing temperature during mixing (X₃), and axial screw force (X₄)—on the response criteria: briquette compressive strength (Y₁), burning time (Y₂), and ash content generated during combustion (Y₃). Based on these models, the corresponding factor–response plots were constructed (Figures 1–6). Accordingly:

The briquette compressive strength is determined by the following regression equation (kg cm⁻²):

      (1)

The burning time of the briquette is determined according to the following regression equation, seconds;

                                   (2)  

The amount of ash produced during briquette burning is determined by the following regression equation, grams;

             (3)   

Using the regression equations obtained for briquette compressive strength (Y₁), burning time (Y₂), and ash content (Y₃), factor–response plots were constructed to show the dependence of each response on the binder fraction (X₁), seed-shell fraction (X₂), processing temperature during mixing (X₃), and axial compaction force of the screw (X₄). The graphical relationships are presented in Figures 1–6.

The effects of the varying factors on the briquette compressive strength (Y₁) are shown in Figures 1 and 2. The effects of the varying factors on briquette burning time (Y₂) are presented in Figures 3 and 4.

Discussion

Analysis of the obtained regression equations and plots—briquette strength across the lower/upper bounds (Figures 1–2), burning time across the lower/upper bounds (Figures 3–4), and ash content generated during combustion across the lower/upper bounds (Figures 5–6)—shows that all factors exert a significant influence on the response criteria. In addition, the binder amount and the axial compaction force of the variable-pitch screw display more complex dependencies than the other investigated factors [9; 11].

To determine the admissible (optimal) values of the responses—briquette compressive strength (Y₁), burning time (Y₂), and ash content during combustion (Y₃)—the regression equations (1)–(3), which relate the responses to the independent variables (binder fraction X₁, seed-shell fraction X₂, processing temperature during mixing X₃, and axial screw compaction force X₄), were solved separately for the briquetting process. The feasible ranges were set as follows: briquette strength 0.5–0.9 kg·cm⁻², burning time 90–110 s, and ash content 10–15%. This multi-criteria task was solved in Excel using the Solver tool (“Поиск решения”), yielding optimal factor values in coded form; these were then converted to natural (physical) units. The coded and natural optimal settings are presented in Table 5. As seen from Table 5 and the graphical relationships, the polynomial and exponential curves at the lower and upper factor bounds yield closely matching values, and the separately solved optimal parameter sets are likewise in close agreement.

Table 5.

Coded and natural values of briquettes based on alcohol waste and paraffin wax with the addition of a binder and fruit pulp

The experimental error does not exceed 5%. Therefore, these settings can be adopted when designing the industrial configuration of the screw-press unit.

Conclusions

Based on the analysis, the optimal settings of the mathematical model describing the effects of the independent variables—binder fraction (X₁), seed-shell fraction (X₂), processing temperature during mixing (X₃), and axial compaction force of the screw (X₄)—on the response criteria—briquette compressive strength (Y₁), burning time (Y₂), and ash content (Y₃)—were standardized as follows:

• Binder fraction: 12%
• Seed-shell fraction: 24%
• Processing temperature during mixing: 96 °C
• Axial screw compaction force: 2.5 kN
• Nozzle (die) diameter: 25 mm

At these settings, the briquettes exhibit: compressive strength с=0,78 kg\cm², burning time t= 110, and ash content 11%. These parameters are recommended for industrial-scale screw-press trials and design.

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