Design of Experiments: Model Development and Optimization of the Cold Crystallization Process in Potash Production

Design of Experiments: Model Development and Optimization of the Cold Crystallization Process in Potash Production | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Design of Experiments: Model Development and Optimization of the Cold Crystallization Process in Potash Production Ye Sun, Ziheng Ma This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7954338/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study aims to optimize the crystallizer operation in a potash production facility at Qinghai Salt Lake by applying the DOE methodology in conjunction with specific experimental data. The objective is to increase production efficiency and product quality. The analysis begins by examining the current state of potash production, highlighting the industry's challenges in improving efficiency, reducing costs, and minimizing environmental impact. Multiple key parameters of the crystallizer process were investigated, including temperature, pressure, agitation speed, and raw material composition. Through multiple rounds of DOE experiments, the critical factors significantly influencing crystallization performance were identified. A corresponding mathematical model was developed and validated. On the basis of this model, optimized operating conditions were proposed to increase the potash crystallization yield while reducing energy consumption and production costs. The advantages and limitations of employing the DOE approach in this context are thoroughly discussed, along with potential directions for future research. Physical sciences/Energy science and technology Physical sciences/Engineering Earth and environmental sciences/Environmental sciences Physical sciences/Materials science Potassium fertilizer production DOE experimental design crystallizer bottom flow concentration Figures Figure 1 Figure 2 Figure 3 1. Introduction In modern agricultural production, potash fertilizer, as one of the three major fertilizers, plays a crucial role in promoting crop growth and increasing yield [ 1 ] . Globally, potash production is concentrated in a few resource-rich countries such as Canada, Russia, and Belarus. These nations possess abundant potash salt deposits, allowing them to dominate the global potash market [ 2 ] . Potash producers continuously optimize production processes, improve efficiency, and expand into international markets to maintain their competitive advantage [ 3 ] . However, with a growing global population and increasing agricultural demand, the need for potash fertilizer continues to rise, placing greater demands on existing production capacity. China’s relatively scarce potash resources have resulted in a heavy reliance on imports. To alleviate this constraint, Chinese potash producers are actively pursuing technological innovation and process optimization to increase the yield and quality of potash fertilizer [ 4 ] . Different production methods have been developed on the basis of practical process effectiveness and application objectives. Common potash production processes generally include flotation, hot leaching crystallization, and cold crystallization. The potash production plant studied in this paper primarily employs a cold crystallization process [ 5 ] . The cold crystallization process is a relatively advanced technique characterized by a complex workflow that requires precise equipment operation and control to ensure optimal performance. During the process, raw materials are first fed into a flotation cell along with chemical reagents to increase the hydrophobicity of sodium chloride, causing it to float to the top of the slurry, thereby effectively separating sodium chloride from potassium chloride. Next, water is added to dissolve the floated material, and the saturation of potassium chloride is achieved through controlled equipment conditions, promoting rapid crystallization. After filtration and washing of the potassium chloride crystals, high-purity potassium chloride is obtained, significantly improving the product quality. The most critical stage of this process is the crystallization phase, whose completion directly determines the quality of the final potash product [ 6 ] . This study focuses on establishing a numerical model of the crystallizer treatment process and proposing specific optimization strategies. 2. Research 2.1 Research Statement Research on the cold crystallization process is not comprehensive, and some literature involving actual production is difficult to access. Scholar Wang Yuzheng et al. noted that temperature and concentration are the most critical control parameters during the crystallization stage. They proposed optimization measures such as multivariable control strategies, model predictive control (MPC), and integrated optimization management, but these methods lack support from specific numerical models [ 7 ] . Huo Yongxing et al., on the basis of actual production conditions, focused solely on the water dosage as a single variable in the crystallization process. Through calculations and comparisons, they reported that the total recovery rate is highest when the water dosage is 46–55% of the weight of the input low-sodium carnallite ore, but they did not comprehensively consider other variables [ 8 ] . Himanshu Patel et al. evaluated the economic feasibility of using solar energy to convert liquid fuels during the crystallization process but did not consider specific optimization schemes for the operational steps [ 9 ] . Basystiuk Ya. et al. focused on separating magnesium chloride from impurities in potassium chloride solutions, obtaining fine crystals through the evaporation of separated sulfates, but they also did not consider other influencing factors in the production process [ 10 ] . In the large-scale production of potash fertilizer, implementing precise control over the production process is crucial. From a practical production standpoint, meticulous regulation of the process is directly linked to the final performance of the potash products. It can increase the quality standards of potash fertilizer and promote the optimization of production efficiency [11]. These positive effects are manifested in multiple dimensions, including improved product purity, reduced impurity content, and effective control of production costs [ 12 ] . In summary, to fully realize the maximum potential of potash production and achieve the optimal balance among quality, efficiency, and cost, it is essential to understand and accurately master the core principles of process control in potash fertilizer production. Building on this understanding, establishing a comprehensive and efficient production process control model is necessary. This model should enable accurate comprehensive evaluation of various factors influencing production outcomes and effectively address bottleneck issues such as low crystallizer processing efficiency and unstable control of underflow concentration [ 13 , 14 ] . 2.2 Research methods Given the large-scale and complex nature of potash production sites, identifying a research method that is low cost, highly efficient, and accurate is essential [ 15 ] . The design of experiments (DOE), as a scientific and efficient experimental approach, has been widely applied to optimize potash production both domestically and internationally. By systematically arranging experiments and analyzing data, the DOE method can quickly identify key factors affecting production and their optimal combinations, thereby enabling the optimization of production conditions (such as water dosage) [ 16 ] . Common DOE methods can be classified into two categories: orthogonal experimental design and factorial design. Orthogonal experiments utilize standardized orthogonal arrays to select experimental conditions, plan and conduct tests, and identify favorable production conditions with a relatively small number of trials. This approach is primarily used to investigate the specific characteristics of complex systems or the effects of multiple factors on certain system properties. Factorial design, also known as factorial experimental design or factorial experiments, is an effective method for studying the effects of two or more varying factors. Many experiments require the investigation of the effects of two or more variable factors. It can be applied to new product development, product or process improvement, and installation services. Through a relatively small number of experiments, it identifies factor combinations that yield high quality, high output, and low consumption, thereby achieving improvement objectives. This study selects the factorial design method and uses Minitab software for experimental design and data analysis [ 17 , 18 ] . Currently, in the potash production process, the DOE method is mostly used for optimizing crystallizer operating parameters, improving process flows, and verifying the reproducibility of production conditions. These applications are relatively systematic and macro scale, with a lack of targeted research focusing on improving production process parameters starting from a single specific way [ 19 ] . During the crystallization stage of potash production, the performance and operating conditions of the crystallizer significantly impact the product yield and quality. Traditional crystallization processes often rely on empirical adjustments and lack scientific theoretical guidance [ 20 ] . To further increase production efficiency, it is necessary to establish a model for component addition in the crystallizer on the basis of the DOE method. This model can comprehensively consider multiple factors, such as raw material characteristics, operating conditions, and environmental factors. By combining numerical simulations with experimental validation, it can predict and optimize material changes and product quality during the crystallization process. Establishing such a model enables precise control over the crystallization process, providing support for process optimization and new product development. In summary, to address the current state and challenges of potash production, this study leverages the design of experiments (DOE) methodology to optimize the production process and establish a model for component addition in a crystallizer. This work aims to increase the efficiency and profitability of potash production while enabling further process refinement. 3. Methods 3.1 Data acquisition Using 2024–2025 operational data from a Golmud-based potash facility, this study develops a component-addition model for the crystallizer by integrating pre- and posttreatment parameter correlations and ranges. The objective is to optimize underflow concentration control and enhance overall production efficiency. 3.2 Data processing 3.2.1 Effective Data selection The production dataset comprises 17 distinct parameters. After excluding invalid entries with missing or erroneous records, a total of 2,325 valid data groups remained. From these, 1% were randomly selected for model validation. The 3σ rule was then applied to the remaining data. In a normal distribution, σ represents the standard deviation, and µ represents the mean, with x = µ being the axis of symmetry. The 3σ principle states that the probability of values falling within (µ-σ, µ + σ) is 0.6827, that within (µ-2σ, µ + 2σ) is 0.9545, and that within (µ-3σ, µ + 3σ) is 0.9973. Therefore, it can be concluded that the Y values of the data are almost entirely concentrated within the (µ-3σ, µ + 3σ) range, with the likelihood of falling outside this interval being less than 0.3%. By applying this principle, the standard deviation and mean for each parameter were calculated. The calculated standard deviations and means for the selected parameters are presented in Table 1 . Table 1 Partial calculation results Parameter KCL in Raw Ore Blended Mother Liquor KCL Hourly Flow Rate (m³/h) Water Specific Gravity On-line Raw Ore Analysis Blended Mother Liquor Crystallizer Underflow Standard Deviation 1.57513895 11.145503 0.319359284 17.96873588 14.72202707 25.33826675 0.083085743 Mean 16.3023237 123.519761 3.80898908 410.1736282 27.59291512 77.00652165 0.350569768 Ultimately, 2189 sets of valid data within the 3σ interval were obtained. 3.2.2 Parameter selection The production dataset comprises 17 parameters. Including all of them in a comprehensive correlation analysis would be overly complex and hinder the derivation of meaningful conclusions. Therefore, a simple linear regression analysis was performed between each parameter and the crystallizer underflow concentration to establish the quantitative relationship between parameter X and the target value Y, thereby identifying parameters with strong correlations for subsequent calculations. The linear regression equation is expressed as follows: Y = a + b*X + e where 'a' is the intercept, 'b' is the correlation coefficient between X and Y, and 'e' is the error term. Through this comparison, seven parameters were selected for further analysis. These seven parameters are as follows: Hourly Ore Throughput (T/h), KCl Content in Raw Ore, Hourly Flow Rate of Blended Mother Liquor (m³/h), KCl Content in the Liquid Phase of Crystallizer Underflow, Volumetric Flow Rate of Crystallizer Underflow (m³/h), Crystallizer Mist Water Flow Rate (m³/h), and Crystallizer Fresh Water Input (m³/h). The statistical results of their regression analysis are presented in Table 2 . Table 2 Results Regres-sion Statisti-cs Multiple R R Square Adjusted R Square Standard Deviation Multiple R R Square Adjusted R Square Standard Error Multiple R R Square Adjust-ed R Square 0.1571 0.02471 0.02426 0.08209 0.5633 0.3173 0.31705 0.0686 0.1930 0.03727 0.036835 In this context, Multiple R represents the 'b' value, Adjusted R Square represents the 'a' value, and the Standard Error represents the 'e' value. 3.3 DOE The core methodology of DOE is as follows: first, screen for key significant factors; second, identify the optimal combination of production conditions; and finally, verify that this optimal combination is reproducible. A total of 2,189 valid data entries for the seven parameters and the target value were input into Minitab 18 to create a factorial design. As this experiment involves seven factors and designs for 2–15 factors typically employ a two-level factorial structure, a design was specified using a generator. The resulting factorial design is presented in Table 3 . Table 3 Factor design results Factor Base Design Resolution Runs Replicates Implementation Fraction Blocks 7 7, 8 Ⅲ 8 1 1/16 1 The dependent variable is the crystallizer underflow concentration. Since there is only a single dependent variable, the total number of center points is set to one. The experimental design adopts 2^n/2 (with n = 7, rounded down) runs, and the run order for each parameter—that is, its execution sequence within the overall experimental design—was randomly generated. The number of blocks is one, indicating that only one set of parameters participates in the experimental design. The design assumes factor interactions among all seven parameters by default, considering the probability of interaction between each pair of factors to be equal when generating the run order. The basic workflow for designing the experiment is as follows: First, the preprocessed raw data are input, and the upper and lower limits for each factor are determined. Then, on the basis of these limits, the standard order and run order for each factor are generated, as shown in Table 4 and Fig. 1 . Table 4 Standard sequence and operational sequence of each factor Standard Order Run Order Center Points Blocks 1 1 1 1 5 2 1 1 9 3 0 1 2 4 1 1 3 5 1 1 7 6 1 1 8 7 1 1 6 8 1 1 4 9 1 1 On the basis of the designed experiment, data meeting the requirements were selected, and eight corresponding tests were conducted under standard laboratory conditions. The resulting crystallizer underflow concentrations were obtained for analysis and modeling. Owing to constraints in experimental conditions, the 3σ rule was applied for data screening. This involved selecting data from the existing 2,189 sets of field data that fell within the ± 3σ error range and closely matched the experimental design requirements. The corresponding crystallizer underflow concentration values of these selected data points were used as the output. The screening results are presented in Table 5 . Table 5 Results Stand-ard Order Run Order Center Points Blocks Parameter KCL in Raw Ore Blended Mother Liquor KCL Hourly Flow Rate (m³/h) Water Specif-ic Gravit-y On-line Raw Ore Analy-sis Blend-ed Moth-er Liquor Crysta-llizer Under-flow 7 1 1 1 126.313 21.7572 178.848 3.03 140.953 81.1319 0.141 0.290238 1 2 1 1 126.313 6.7409 93.48 4.76 436.544 81.1319 0.141 0.418368 4 3 1 1 518.923 21.7572 93.48 4.76 140.953 0.4318 0.141 0.302927 6 4 1 1 518.923 6.7409 178.848 3.03 436.544 0.4318 0.141 0.297765 3 5 1 1 126.313 21.7572 93.48 3.03 436.544 0.4318 148.723 0.425328 8 6 1 1 518.923 21.7572 178.848 4.76 436.544 81.1319 148.723 0.345428 5 7 1 1 126.313 6.7409 178.848 4.76 140.953 0.4318 148.723 0.49692 2 8 1 1 518.923 6.7409 93.48 3.03 140.953 81.1319 148.723 0.419777 4. Results 4.1 Model establishment Pareto optimality refers to an ideal state of resource allocation. In this experiment, a Pareto effect analysis was first conducted for each parameter factor, which is an analysis of the degree to which each parameter factor optimizes the final output. The results are shown in Fig. 2 . The chart features the effect analysis of the crystallizer underflow concentration on the horizontal axis. The vertical axis represents the following independent parameters: Hourly Ore Throughput (T/h), KCl Content in Raw Ore, Hourly Flow Rate of Blended Mother Liquor (m³/h), KCl Content in the Liquid Phase of Crystallizer Underflow, Volumetric Flow Rate of Crystallizer Underflow (m³/h), Crystallizer Mist Water Flow Rate (m³/h), and Crystallizer Fresh Water Input (m³/h). A two-sided confidence interval was applied with a significance level of α = 0.05. The analysis indicates that crystallizer fresh water input has the greatest effect on the dependent variable. The influences of the hourly Ore Throughput and KCl content in the Raw Ore are similar in magnitude, whereas the effects of the remaining factors are relatively minor. In response to these findings, a mixed-effects model incorporating these three key factors was established as a reference to increase modeling accuracy. 4.2 Three-factor Mixed Effects Model The hourly ore throughput (T/h), KCl content in raw ore, hourly flow rate of blended mother liquor (m³/h), KCl content in the liquid phase of crystallizer underflow, volumetric flow rate of crystallizer underflow (m³/h), crystallizer mist water flow rate (m³/h), and crystallizer fresh water input (m³/h) are denoted by the letters A to G, respectively, while the crystallizer underflow concentration is designated Y for subsequent computational convenience. A mixed-effects model was established for three factors: crystallizer fresh water input, hourly ore throughput, and KCl content in raw ore. The corresponding error analysis results are presented in Table 6 . Table 6 Model error analysis Generally, the p value represents the probability of obtaining the observed results, or more extreme ones, assuming that the null hypothesis is true. If the p value is less than the selected significance level (α = 0.05), the null hypothesis is rejected. The Z value measures the number of standard deviations by which a sample mean deviates from the population mean. The coefficients for the overall model are presented in Table 7 . Variance Group Variable Proportion SD Z P A 0.001893 20.53% 0.003110 0.608757 0.271 B 0.001959 21.24% 0.003203 0.611659 0.270 G 0.004168 45.19% 0.006323 0.659153 0.255 Error 0.001203 13.04% 0.000851 1.414214 0.079 Total 0.009223 −2Log=−18.414135 Table 7 Three-factor mixed effects model Coefficient Group Coefficient SD Free degree T P Con 0.374594 0.064502 2.31 5.807491 0.020 When the P value is less than or equal to the alpha (α) value, the differences between some of the means are considered statistically significant. On the basis of the results, since the P value is less than the significance level of 0.05, we conclude that the model is unacceptable. 4.3 Overall Model A model for 7 parameters was constructed, and variance analysis was performed on the model. Table 8 Analysis of variance Variance Analysis Group Free degree Adj SS Adj MS Model 7 0.040501 0.005786 Linearity 7 0.040501 0.005786 A 1 0.008775 0.008775 B 1 0.009039 0.009039 C 1 0.002314 0.002314 D 1 0.002130 0.002130 E 1 0.000066 0.000066 F 1 0.000302 0.000302 G 1 0.017875 0.017875 Error 0 Total 7 0.040501 Adj MS = Adj SS/Degrees of Freedom, which is termed the Adjusted Mean Square. Adj SS, the adjusted sum of squares, represents the total sum of squares. It is the sum of the sum of squares for the model and the sum of squares for error, thereby quantifying the total variation in the data. Since the corresponding P values for both are below the significance level of 0.05, the results are considered acceptable. Through calculation, the final data model is derived as follows: Y = 0.4854-0.000169*A-0.004477*B-0.000398*C + 0.01886*D-0.000019*E-0.000152*F + 0.04727*G Substituting the parameter names yields the complete model: Crystallizer Underflow Concentration = 0.4854–0.000169 × Hourly Ore Throughput − 0.004477 × KCl Content in Raw Ore − 0.000398 × Hourly Flow Rate of Blended Mother Liquor + 0.01886 × KCl Content in Liquid Phase of Crystallizer Underflow − 0.000019 × Volumetric Flow Rate of Crystallizer Underflow − 0.000152 × Crystallizer Mist Water Flow Rate + 0.04727 × Crystallizer Fresh Water Input 4.4 Model Validation The overall model was validated via 23 sets of valid data that were withheld from the model development process. Following the calculation of the results, error analysis was performed between the computed crystallizer underflow concentration data and the original measured data. This analysis included an evaluation of the root mean square error (RMSE) and the coefficient of determination (R²). The results are shown in Fig. 3 . 4.4.1 RMSE analysis RMSE =​ \(\:\sqrt{\text{1/}\text{n}\text{∗}\sum\:_{\text{i}\text{=1}}^{\text{n}}\text{（}{\text{y}}_{\text{i}}\text{−}{\text{y}{\prime\:}}_{\text{i}}\text{)^2}}\) n represents the number of data points, y i is the data point in the original dataset, and ŷ i is the corresponding data point in the compared dataset. The calculated RMSE value is 0.014. A smaller RMSE indicates a better fit between the formula and the original data. This result demonstrates a good level of fit for the formula. 4.4.2 R^2 Analysis R^2 = \(\:\sum\:_{\text{i}\text{=1}}\text{(}{\text{y}}_{\text{i}}\text{−}{\stackrel{\text{ˇ}}{\text{y}}}_{}\) )( \(\:{\text{y}{\prime\:}}_{\text{i}}\) - \(\:{\stackrel{\text{ˇ}}{\text{y}{\prime\:}}}_{}\) )/ \(\:\sqrt{\sum\:_{\text{i}\text{=1}}\text{(}{\text{y}}_{\text{i}}\text{−}{\stackrel{\text{ˇ}}{\text{y}}}_{}\text{)^2∗}\sum\:_{\text{i=1}}\text{(}{\text{y}{\prime\:}}_{\text{i}}\text{−}{\stackrel{\text{ˇ}}{\text{y}{\prime\:}}}_{}\text{)}\text{^2}}\) In the formula, y i is the data point in the original dataset, ŷ i is the corresponding data point in the compared dataset, \(\:{\stackrel{\text{ˇ}}{\text{y}}}_{}\) is the mean of the original dataset, and \(\:{\stackrel{\text{ˇ}}{\text{y}{\prime\:}}}_{}\) is the mean of the compared dataset. R² is used to evaluate the correlation between the formula-calculated data and the original data. A value of R² closer to 1 indicates a better fit of the formula. The calculated result is 0.7443, which demonstrates a good level of fit for the formula. 5. Discussion On the basis of actual production data from a potash fertilizer manufacturing site, this study utilized the DOE methodology to perform an optimization analysis of key parameters in the crystallizer treatment process. Through preliminary data screening, correlation analysis, and experimental design, seven key parameters were identified, including the hourly ore throughput (T/h), the KCl content in the raw ore, the hourly flow rate of the blended mother liquor (m³/h), the KCl content in the liquid phase of the crystallizer underflow, the volumetric flow rate of the crystallizer underflow (m³/h), the crystallizer mist water flow rate (m³/h), and the crystallizer freshwater input rate (m³/h). A systematic factorial design experiment was subsequently conducted for these parameters via Minitab 18 software, followed by an in-depth analysis of the experimental results. Pareto analysis revealed that the Crystallizer Freshwater Input has the most significant effect on the crystallizer underflow concentration. This finding underscores the critical importance of precise control over freshwater addition in enhancing the production efficiency and quality of potash fertilizer. Furthermore, the effects of Hourly Ore Throughput and the KCl Content in Raw Ore were found to be comparable in magnitude and significant, indicating that these parameters likewise play crucial roles in maintaining production stability and product quality. A tentative mixed-effects model incorporating the three most influential parameters was developed. However, the analysis of variance (ANOVA) results for this model showed a P value greater than the significance level of 0.05, indicating that the model was not statistically significant at the current threshold. Through further comprehensive model analysis, a mathematical model incorporating all seven parameters was derived to predict the crystallizer underflow concentration. The ANOVA results demonstrated that both the total sum of squares and the error sum of squares were associated with P values below the 0.05 significance level, confirming the statistical reliability of the model. The model equation is as follows: Crystallizer Underflow Concentration = 0.4854–0.000169 × Hourly Ore Throughput − 0.004477 × KCl Content in Raw Ore − 0.000398 × Hourly Flow Rate of Blended Mother Liquor + 0.01886 × KCl Content in Liquid Phase of Crystallizer Underflow − 0.000019 × Volumetric Flow Rate of Crystallizer Underflow − 0.000152 × Crystallizer Mist Water Flow Rate + 0.04727 × Crystallizer Fresh Water Input This model effectively captures the influence of various parameters on the crystallizer underflow concentration during production, providing a scientific theoretical basis for process optimization. It can be used not only to predict the crystallizer underflow concentration but also to simulate the crystallization performance under different production conditions by adjusting the parameter values within the model, thereby identifying the optimal combination of production parameters. Furthermore, the model can be employed for real-time monitoring of changes in key process parameters, helping to ensure operational stability and consistent product quality. The main contributions and innovations of this paper include the following: Identification of Key Parameters: Through effective screening of production data and correlation analysis, seven key parameters influencing the crystallizer underflow concentration were successfully identified. Pareto analysis: Pareto analysis demonstrated that the fresh water input of the crystallizer has the most significant effect on the underflow concentration, with the hourly ore throughput and the KCl content in the raw ore also highly influential. Model development and optimization: On the basis of the DOE experimental design, a mathematical model incorporating all seven parameters was established to predict the crystallizer underflow concentration. The model's validity was confirmed via analysis of variance (ANOVA). Systematic analytical methodology: This research provides a systematic and comprehensive analysis and optimization of multiple key parameters in the potash fertilizer production crystallizer process. The methodology, involving screening and correlation analysis, enables relatively accurate prediction of the crystallizer underflow concentration. Investigation of Multifactor Interactions: This study considered not only the individual effects of single parameters on the crystallizer underflow concentration but also the interactions between multiple parameters, offering valuable insights for optimizing complex production systems. On the basis of the findings of this study, the following production optimization recommendations are proposed: Optimize the Crystallizer Freshwater Input: Given that the fresh water input has the most significant effect on the crystallizer underflow concentration, precise control of this parameter should be enhanced to reduce variability and improve product quality. Monitoring the Hourly Ore Throughput and Raw Ore KCl Contents: Although the influence of these two parameters is secondary to the freshwater input, their stability is equally crucial for smooth process operation. They should be regularly monitored and adjusted to remain within optimal ranges. To comprehensively consider other parameters, while the remaining parameters have a lesser individual impact on the underflow concentration, their variations should still be fully considered in actual production to maximize overall production efficiency. Implementing continuous monitoring and feedback: Establish a robust production monitoring system for real-time tracking and logging of all key parameters. The process parameters should be promptly adjusted on the basis of the monitoring results to ensure process stability and controllable product quality. Given the complexity and diversity of potash fertilizer production processes, while this study has achieved certain results, further in-depth research and improvement are necessary. Future work involving more experimentation and data analysis can further optimize the production model and enhance efficiency: Model Refinement and Validation: Future research should focus on increasing the sample size to reduce the impact of data variability on the model outcomes and incorporate more potential influencing factors to improve the model's accuracy and reliability. Concurrently, the model requires validation within actual production environments to ensure its effectiveness in practical applications. Research on Green Production Processes: As environmental regulations become increasingly stringent, future studies should also address environmental concerns in potash production. This can be achieved by optimizing production processes and introducing green production technologies to reduce energy consumption and environmental pollution, ultimately achieving sustainable development. Comprehensive Optimization Research: Beyond the crystallizer treatment process, the DOE methodology can be applied to other stages of potash production, such as raw material pretreatment and evaporation crystallization, to achieve integrated optimization of the entire production chain. In summary, this study provides foundational support for the optimization of the potash production process. Future research will continue to explore areas such as model refinement and the development of intelligent control systems. Declarations Author contributions statement Author 1 (First Author): Ye Sun, conceptualization, methodology, software, investigation, formal analysis, writing - original draft, corresponding author; Author 2: Ziheng Ma, Data Curation, Writing - Review & Editing, Visualization, Investigation; Conflict of interest statement All the authors disclosed no relevant relationships. Funding Source Declaration This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Data A vailability S tatement All data generated or analysed during this study are included in this published article [and its supplementary information files]. References Li, Y., Ma, Z. & Song, X. New Advances in the Development of Potassium Resources from Qinghai Chloride-Type Salt Lakes and Suggestions for Industrial Development. Inorg. Chemicals Ind. ( 08 ), (2023). He, F. & Gao, C. Application of Common Salt Lake Potassium Chloride Production Processes. Chem. Manage. ( 06 ), (2023). Cheng, P. Study on Process Control of Potassium Chloride Production by Reverse Flotation-Cold Crystallization. China Petroleum Chem. Standard Qual. ( 24 ), (2022). Lei, B. & Chen, M. Comprehensive Energy Consumption Analysis and Countermeasures for Potassium Chloride Production. Salt Sci. Chem. Ind. ( 08 ), (2022). Guo, Y., Liu, Q. & Li, X. Research on Optimization of Energy-Saving Equipment in Hot Leaching-Crystallization Potassium Chloride Production Process. Chem. Manage. ( 36 ), (2021). Li, Y., Wang, N. & Liu, X. Equipment and Process for Potassium Chloride Production Crystallization. Chem. Manage. ( 11 ), (2021). Wang, Y. & Yang, M. Study on Process Control of Potassium Chloride Production by Reverse Flotation-Cold Crystallization. Chem. Eng. Des. Commun. 50 (08), 7–9 (2024). Huo, Y. et al. Control of Water Addition in Cold Crystallization Step of Potassium Chloride by Reverse Flotation-Cold Crystallization Method. Salt Sci. Chem. Ind. 52 (12), 26–30 (2023). Patel, H., Müller, F., Maiti, P. & Maiti, S. Economic evaluation of solar-driven thermochemical conversion of empty cotton boll biomass to syngas and potassic fertilizer. Energy. Conv. Manag. 209 , 112631 (2020). Basystiuk, Y. I. & Kostiv, I. Y. Getting Hydrated Magnesium Chloride from Magnesium Chloride Solutions of Potassium Sulfate Fertilizers Production. J. Chem. Eng. Process. Technol. 7 (2), 1–4 (2016). Wang, L., Xu, Y., Chen, H. & Song, X. New insights into octadecylamine-monoacid selective adsorption on KCl/NaCl surface: Experimental and molecular dynamic simulation. Appl. Surf. Sci. (2021). Zhong, A. et al. Atomic insights into flotation separation of KCl and NaCl from a new viewpoint of hydration layer: A molecular dynamic study. Colloids and Surfaces A: Physicochemical and Engineering Aspects (2020). Huang, Z. et al. Evaluation of a novel morpholine-typed Gemini surfactant as the collector for the reverse flotation separation of halite from carnal lite ore. J. Mol. Liq. (2020). Wang, P. L. K., Hsiao, C. C. & Ho, K. C. Y. C. Optimization of Nd:YAG laser welding onto magnesium alloy via Taguchi analysis. Opt. Laser Technol. ( 04 ), (2014). Wang, X. et al. Technological Progress in Potassium Extraction from Qinghai Salt Lakes and the Development of China's Potash Fertilizer Industry. Chem. Minerals Process. ( 11 ), (2017). Ma, F. Six Sigma Management Statistical Guide (Renmin University of China, 2018). Kempe, M. D., Jorgensen, G. J., Terwilliger, K. M., McMahon, T. J. & Kennedy, C. E. & Borek T. T. Acetic acid production and glass transition concerns with ethylene-vinyl acetate used in photovoltaic devices. Sol. Energy Mater. Sol. Cells ( 04 ), (2016). Min, Y. Design of Experiments (DOE) Application Guide (China Machine, 2011). Tan, S. Insights from Domestic and Foreign Practices in Comprehensive Development and Utilization of Salt Lake Resources for Qinghai Salt Lake Resources. Salt Sci. Chem. Ind. ( 08 ), (2017). Wang, H. Multscale Coupling Model and Optimization Study on the Preparation Process of Potassium Chloride and Magnesium Chloride Hydrates (Tianjin University of Science and Technology, 2014). Additional Declarations No competing interests reported. Supplementary Files DOE.xlsx .8.xlsx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7954338","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":542765035,"identity":"8a049190-bd6b-4971-bfb2-88507d0cce68","order_by":0,"name":"Ye Sun","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxklEQVRIiWNgGAWjYBAC+wMHGx8k8NTY8bM3EKvn4OFmgw8yx5Ilew4Qq+Xw8TbJGTbMjBtmJBCpg7HtYJs0Tw4bs4Hk4403GGpsoglqYeY52GzNc0aGz1w6rdiC4VhabgMhLWwSBxtv8/awMVvOzjGTYGw4TFgLj/zDBmnef0C/3DxDpBYJhoNNkjN4gFpu8BCpxYDhIDCQeUCBDPRLAjF+MWA4/hAalYc33vhQY0NYC4p2iQRSlEO0kKpjFIyCUTAKRgYAACGEQagX627vAAAAAElFTkSuQmCC","orcid":"","institution":"Central Iron \u0026 Steel Research Institute","correspondingAuthor":true,"prefix":"","firstName":"Ye","middleName":"","lastName":"Sun","suffix":""},{"id":542765036,"identity":"5b7ce54b-df78-4feb-af0f-908d36bb8f25","order_by":1,"name":"Ziheng Ma","email":"","orcid":"","institution":"Central South University","correspondingAuthor":false,"prefix":"","firstName":"Ziheng","middleName":"","lastName":"Ma","suffix":""}],"badges":[],"createdAt":"2025-10-27 11:34:05","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7954338/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7954338/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96363894,"identity":"6f787ddc-f623-41d3-b40b-aa1d9334844a","added_by":"auto","created_at":"2025-11-20 10:08:22","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":162887,"visible":true,"origin":"","legend":"","description":"","filename":"DesignofExperimentsModelDevelopmentandOptimizationoftheColdCrystallizationProcessinPotashProduction.doc.docx","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/6d39f8d4947a9192b49077dc.docx"},{"id":96275016,"identity":"8ba254ee-a82d-4a5a-b416-abcab3105539","added_by":"auto","created_at":"2025-11-19 09:54:51","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3958,"visible":true,"origin":"","legend":"","description":"","filename":"a66d3003fe7b4c9ebd622d733f7122f2.json","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/33a92ed830cd1ee3205702eb.json"},{"id":96275052,"identity":"b6b16000-3e3e-4498-a966-438f141eb6cd","added_by":"auto","created_at":"2025-11-19 09:54:54","extension":"xlsx","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":15488,"visible":true,"origin":"","legend":"","description":"","filename":"DOEd1.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/8ca198dc90046802e1271e68.xlsx"},{"id":96365025,"identity":"61ee9c3e-a385-4cda-a766-a3a8088a697b","added_by":"auto","created_at":"2025-11-20 10:09:56","extension":"xlsx","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":406107,"visible":true,"origin":"","legend":"","description":"","filename":".8d1.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/73346d477cecdbbd2fc94f25.xlsx"},{"id":96275027,"identity":"0310490c-8984-4233-b6fc-9122e048e2f0","added_by":"auto","created_at":"2025-11-19 09:54:51","extension":"xml","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":93198,"visible":true,"origin":"","legend":"","description":"","filename":"a66d3003fe7b4c9ebd622d733f7122f21enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/11dddd5b7cd940c3053055f6.xml"},{"id":96275022,"identity":"27ecb865-2954-43ab-95c4-d2ad90f3023d","added_by":"auto","created_at":"2025-11-19 09:54:51","extension":"png","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":8551,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/587fc608db92d226c074be76.png"},{"id":96275023,"identity":"b970ce27-ad6d-4333-9d37-824c99a2b44a","added_by":"auto","created_at":"2025-11-19 09:54:51","extension":"png","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":14751,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/a441a48f6aacead1e710066c.png"},{"id":96275018,"identity":"91f53894-f4ee-4c7c-895a-40dd5ff4cbad","added_by":"auto","created_at":"2025-11-19 09:54:51","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":9648,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/da9d1626f5f68968772625ea.png"},{"id":96275029,"identity":"de5fbd97-c786-4880-8ba0-5cc2bd8e68a6","added_by":"auto","created_at":"2025-11-19 09:54:51","extension":"xml","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":92231,"visible":true,"origin":"","legend":"","description":"","filename":"a66d3003fe7b4c9ebd622d733f7122f21structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/04e4c8cdbe483f6c7b24daed.xml"},{"id":96364087,"identity":"b602b477-ad1a-4842-bb6f-dbb1fc70b7e2","added_by":"auto","created_at":"2025-11-20 10:08:51","extension":"html","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":97987,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/38b712c94c2fc907056f06ec.html"},{"id":96275021,"identity":"4edb049d-cea5-4ea3-9fae-84b9830cb808","added_by":"auto","created_at":"2025-11-19 09:54:51","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":14110,"visible":true,"origin":"","legend":"\u003cp\u003eAvailable factor design.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/9322ad03219fb0261c0f3853.png"},{"id":96364065,"identity":"9e96608b-8927-4bdf-87cb-2b3100b053ca","added_by":"auto","created_at":"2025-11-20 10:08:49","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":32117,"visible":true,"origin":"","legend":"\u003cp\u003ePareto effect analysis.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/50043af673b18e99a5c753e9.png"},{"id":96363686,"identity":"8b644338-5e8e-488b-81e1-d4a3f47770b8","added_by":"auto","created_at":"2025-11-20 10:07:44","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":60135,"visible":true,"origin":"","legend":"\u003cp\u003eRaw data and computational data.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/fd3f6dcb8ca53527c964ba55.jpeg"},{"id":107382321,"identity":"0bed1c77-eef6-4f93-baf2-1903edb9a4a8","added_by":"auto","created_at":"2026-04-21 02:55:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":732104,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/4149c782-bf6d-4eca-89fd-3fc52f840872.pdf"},{"id":96275017,"identity":"832d8671-4272-4645-9a84-f305e91411b7","added_by":"auto","created_at":"2025-11-19 09:54:51","extension":"xlsx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":15488,"visible":true,"origin":"","legend":"","description":"","filename":"DOE.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/26b30610be0b44fa218178cc.xlsx"},{"id":96275025,"identity":"3df4fbed-25b9-481b-b875-c630f4e4c971","added_by":"auto","created_at":"2025-11-19 09:54:51","extension":"xlsx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":406107,"visible":true,"origin":"","legend":"","description":"","filename":".8.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-7954338/v1/c7a0603efa1870040a4f8093.xlsx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Design of Experiments: Model Development and Optimization of the Cold Crystallization Process in Potash Production","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn modern agricultural production, potash fertilizer, as one of the three major fertilizers, plays a crucial role in promoting crop growth and increasing yield \u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e. Globally, potash production is concentrated in a few resource-rich countries such as Canada, Russia, and Belarus. These nations possess abundant potash salt deposits, allowing them to dominate the global potash market \u003csup\u003e[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]\u003c/sup\u003e. Potash producers continuously optimize production processes, improve efficiency, and expand into international markets to maintain their competitive advantage \u003csup\u003e[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eHowever, with a growing global population and increasing agricultural demand, the need for potash fertilizer continues to rise, placing greater demands on existing production capacity. China\u0026rsquo;s relatively scarce potash resources have resulted in a heavy reliance on imports. To alleviate this constraint, Chinese potash producers are actively pursuing technological innovation and process optimization to increase the yield and quality of potash fertilizer \u003csup\u003e[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eDifferent production methods have been developed on the basis of practical process effectiveness and application objectives. Common potash production processes generally include flotation, hot leaching crystallization, and cold crystallization. The potash production plant studied in this paper primarily employs a cold crystallization process \u003csup\u003e[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eThe cold crystallization process is a relatively advanced technique characterized by a complex workflow that requires precise equipment operation and control to ensure optimal performance. During the process, raw materials are first fed into a flotation cell along with chemical reagents to increase the hydrophobicity of sodium chloride, causing it to float to the top of the slurry, thereby effectively separating sodium chloride from potassium chloride. Next, water is added to dissolve the floated material, and the saturation of potassium chloride is achieved through controlled equipment conditions, promoting rapid crystallization. After filtration and washing of the potassium chloride crystals, high-purity potassium chloride is obtained, significantly improving the product quality. The most critical stage of this process is the crystallization phase, whose completion directly determines the quality of the final potash product \u003csup\u003e[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/sup\u003e. This study focuses on establishing a numerical model of the crystallizer treatment process and proposing specific optimization strategies.\u003c/p\u003e"},{"header":"2. Research","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Research Statement\u003c/h2\u003e\u003cp\u003eResearch on the cold crystallization process is not comprehensive, and some literature involving actual production is difficult to access. Scholar Wang Yuzheng et al. noted that temperature and concentration are the most critical control parameters during the crystallization stage. They proposed optimization measures such as multivariable control strategies, model predictive control (MPC), and integrated optimization management, but these methods lack support from specific numerical models \u003csup\u003e[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/sup\u003e. Huo Yongxing et al., on the basis of actual production conditions, focused solely on the water dosage as a single variable in the crystallization process. Through calculations and comparisons, they reported that the total recovery rate is highest when the water dosage is 46\u0026ndash;55% of the weight of the input low-sodium carnallite ore, but they did not comprehensively consider other variables \u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e. Himanshu Patel et al. evaluated the economic feasibility of using solar energy to convert liquid fuels during the crystallization process but did not consider specific optimization schemes for the operational steps \u003csup\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e. Basystiuk Ya. et al. focused on separating magnesium chloride from impurities in potassium chloride solutions, obtaining fine crystals through the evaporation of separated sulfates, but they also did not consider other influencing factors in the production process \u003csup\u003e[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eIn the large-scale production of potash fertilizer, implementing precise control over the production process is crucial. From a practical production standpoint, meticulous regulation of the process is directly linked to the final performance of the potash products. It can increase the quality standards of potash fertilizer and promote the optimization of production efficiency [11]. These positive effects are manifested in multiple dimensions, including improved product purity, reduced impurity content, and effective control of production costs \u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eIn summary, to fully realize the maximum potential of potash production and achieve the optimal balance among quality, efficiency, and cost, it is essential to understand and accurately master the core principles of process control in potash fertilizer production. Building on this understanding, establishing a comprehensive and efficient production process control model is necessary. This model should enable accurate comprehensive evaluation of various factors influencing production outcomes and effectively address bottleneck issues such as low crystallizer processing efficiency and unstable control of underflow concentration \u003csup\u003e[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Research methods\u003c/h2\u003e\u003cp\u003eGiven the large-scale and complex nature of potash production sites, identifying a research method that is low cost, highly efficient, and accurate is essential \u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]\u003c/sup\u003e. The design of experiments (DOE), as a scientific and efficient experimental approach, has been widely applied to optimize potash production both domestically and internationally. By systematically arranging experiments and analyzing data, the DOE method can quickly identify key factors affecting production and their optimal combinations, thereby enabling the optimization of production conditions (such as water dosage) \u003csup\u003e[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/sup\u003e. Common DOE methods can be classified into two categories: orthogonal experimental design and factorial design.\u003c/p\u003e\u003cp\u003eOrthogonal experiments utilize standardized orthogonal arrays to select experimental conditions, plan and conduct tests, and identify favorable production conditions with a relatively small number of trials. This approach is primarily used to investigate the specific characteristics of complex systems or the effects of multiple factors on certain system properties.\u003c/p\u003e\u003cp\u003eFactorial design, also known as factorial experimental design or factorial experiments, is an effective method for studying the effects of two or more varying factors. Many experiments require the investigation of the effects of two or more variable factors. It can be applied to new product development, product or process improvement, and installation services. Through a relatively small number of experiments, it identifies factor combinations that yield high quality, high output, and low consumption, thereby achieving improvement objectives. This study selects the factorial design method and uses Minitab software for experimental design and data analysis \u003csup\u003e[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eCurrently, in the potash production process, the DOE method is mostly used for optimizing crystallizer operating parameters, improving process flows, and verifying the reproducibility of production conditions. These applications are relatively systematic and macro scale, with a lack of targeted research focusing on improving production process parameters starting from a single specific way \u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eDuring the crystallization stage of potash production, the performance and operating conditions of the crystallizer significantly impact the product yield and quality. Traditional crystallization processes often rely on empirical adjustments and lack scientific theoretical guidance \u003csup\u003e[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e. To further increase production efficiency, it is necessary to establish a model for component addition in the crystallizer on the basis of the DOE method. This model can comprehensively consider multiple factors, such as raw material characteristics, operating conditions, and environmental factors. By combining numerical simulations with experimental validation, it can predict and optimize material changes and product quality during the crystallization process. Establishing such a model enables precise control over the crystallization process, providing support for process optimization and new product development.\u003c/p\u003e\u003cp\u003eIn summary, to address the current state and challenges of potash production, this study leverages the design of experiments (DOE) methodology to optimize the production process and establish a model for component addition in a crystallizer. This work aims to increase the efficiency and profitability of potash production while enabling further process refinement.\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Methods","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Data acquisition\u003c/h2\u003e\u003cp\u003eUsing 2024\u0026ndash;2025 operational data from a Golmud-based potash facility, this study develops a component-addition model for the crystallizer by integrating pre- and posttreatment parameter correlations and ranges. The objective is to optimize underflow concentration control and enhance overall production efficiency.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Data processing\u003c/h2\u003e\u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\u003ch2\u003e3.2.1 Effective Data selection\u003c/h2\u003e\u003cp\u003eThe production dataset comprises 17 distinct parameters. After excluding invalid entries with missing or erroneous records, a total of 2,325 valid data groups remained. From these, 1% were randomly selected for model validation. The 3σ rule was then applied to the remaining data.\u003c/p\u003e\u003cp\u003eIn a normal distribution, σ represents the standard deviation, and \u0026micro; represents the mean, with x\u0026thinsp;=\u0026thinsp;\u0026micro; being the axis of symmetry. The 3σ principle states that the probability of values falling within (\u0026micro;-σ, \u0026micro;\u0026thinsp;+\u0026thinsp;σ) is 0.6827, that within (\u0026micro;-2σ, \u0026micro;\u0026thinsp;+\u0026thinsp;2σ) is 0.9545, and that within (\u0026micro;-3σ, \u0026micro;\u0026thinsp;+\u0026thinsp;3σ) is 0.9973. Therefore, it can be concluded that the Y values of the data are almost entirely concentrated within the (\u0026micro;-3σ, \u0026micro;\u0026thinsp;+\u0026thinsp;3σ) range, with the likelihood of falling outside this interval being less than 0.3%. By applying this principle, the standard deviation and mean for each parameter were calculated. The calculated standard deviations and means for the selected parameters are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePartial calculation results\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eParameter\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eKCL in Raw Ore\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eBlended Mother Liquor KCL\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHourly Flow Rate\u003c/p\u003e\u003cp\u003e(m\u0026sup3;/h)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eWater Specific Gravity\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eOn-line Raw Ore Analysis\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eBlended Mother Liquor\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eCrystallizer Underflow\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStandard Deviation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.57513895\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e11.145503\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.319359284\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e17.96873588\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e14.72202707\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e25.33826675\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.083085743\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMean\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e16.3023237\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e123.519761\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.80898908\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e410.1736282\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e27.59291512\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e77.00652165\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.350569768\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eUltimately, 2189 sets of valid data within the 3σ interval were obtained.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\u003ch2\u003e3.2.2 Parameter selection\u003c/h2\u003e\u003cp\u003eThe production dataset comprises 17 parameters. Including all of them in a comprehensive correlation analysis would be overly complex and hinder the derivation of meaningful conclusions. Therefore, a simple linear regression analysis was performed between each parameter and the crystallizer underflow concentration to establish the quantitative relationship between parameter X and the target value Y, thereby identifying parameters with strong correlations for subsequent calculations.\u003c/p\u003e\u003cp\u003eThe linear regression equation is expressed as follows:\u003c/p\u003e\u003cp\u003eY\u0026thinsp;=\u0026thinsp;a\u0026thinsp;+\u0026thinsp;b*X\u0026thinsp;+\u0026thinsp;e\u003c/p\u003e\u003cp\u003ewhere 'a' is the intercept, 'b' is the correlation coefficient between X and Y, and 'e' is the error term. Through this comparison, seven parameters were selected for further analysis. These seven parameters are as follows: Hourly Ore Throughput (T/h), KCl Content in Raw Ore, Hourly Flow Rate of Blended Mother Liquor (m\u0026sup3;/h), KCl Content in the Liquid Phase of Crystallizer Underflow, Volumetric Flow Rate of Crystallizer Underflow (m\u0026sup3;/h), Crystallizer Mist Water Flow Rate (m\u0026sup3;/h), and Crystallizer Fresh Water Input (m\u0026sup3;/h).\u003c/p\u003e\u003cp\u003eThe statistical results of their regression analysis are presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eResults\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"12\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegres-sion Statisti-cs\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMultiple R\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eR Square\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eAdjusted R Square\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eStandard Deviation\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMultiple R\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eR Square\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eAdjusted R Square\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e\u003cp\u003eStandard Error\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c10\"\u003e\u003cp\u003eMultiple R\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c11\"\u003e\u003cp\u003eR Square\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c12\"\u003e\u003cp\u003eAdjust-ed R Square\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.1571\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.02471\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.02426\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.08209\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.5633\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.3173\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.31705\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.0686\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.1930\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0.03727\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e0.036835\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eIn this context, Multiple R represents the 'b' value, Adjusted R Square represents the 'a' value, and the Standard Error represents the 'e' value.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.3 DOE\u003c/h2\u003e\u003cp\u003eThe core methodology of DOE is as follows: first, screen for key significant factors; second, identify the optimal combination of production conditions; and finally, verify that this optimal combination is reproducible.\u003c/p\u003e\u003cp\u003eA total of 2,189 valid data entries for the seven parameters and the target value were input into Minitab 18 to create a factorial design. As this experiment involves seven factors and designs for 2\u0026ndash;15 factors typically employ a two-level factorial structure, a design was specified using a generator. The resulting factorial design is presented in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eFactor design results\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFactor\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBase Design\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eResolution\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eRuns\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eReplicates\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eImplementation Fraction\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eBlocks\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e7, 8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eⅢ\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1/16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe dependent variable is the crystallizer underflow concentration. Since there is only a single dependent variable, the total number of center points is set to one. The experimental design adopts 2^n/2 (with n\u0026thinsp;=\u0026thinsp;7, rounded down) runs, and the run order for each parameter\u0026mdash;that is, its execution sequence within the overall experimental design\u0026mdash;was randomly generated. The number of blocks is one, indicating that only one set of parameters participates in the experimental design. The design assumes factor interactions among all seven parameters by default, considering the probability of interaction between each pair of factors to be equal when generating the run order.\u003c/p\u003e\u003cp\u003eThe basic workflow for designing the experiment is as follows: First, the preprocessed raw data are input, and the upper and lower limits for each factor are determined. Then, on the basis of these limits, the standard order and run order for each factor are generated, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eStandard sequence and operational sequence of each factor\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStandard Order\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRun Order\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCenter Points\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eBlocks\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eOn the basis of the designed experiment, data meeting the requirements were selected, and eight corresponding tests were conducted under standard laboratory conditions. The resulting crystallizer underflow concentrations were obtained for analysis and modeling. Owing to constraints in experimental conditions, the 3σ rule was applied for data screening. This involved selecting data from the existing 2,189 sets of field data that fell within the \u0026plusmn;\u0026thinsp;3σ error range and closely matched the experimental design requirements. The corresponding crystallizer underflow concentration values of these selected data points were used as the output. The screening results are presented in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eResults\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"12\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStand-ard Order\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRun Order\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCenter Points\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eBlocks\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eParameter\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eKCL in Raw Ore\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eBlended Mother Liquor KCL\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eHourly Flow Rate\u003c/p\u003e\u003cp\u003e(m\u0026sup3;/h)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e\u003cp\u003eWater Specif-ic Gravit-y\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c10\"\u003e\u003cp\u003eOn-line Raw Ore Analy-sis\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c11\"\u003e\u003cp\u003eBlend-ed Moth-er Liquor\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c12\"\u003e\u003cp\u003eCrysta-llizer Under-flow\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e126.313\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e21.7572\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e178.848\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e3.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e140.953\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e81.1319\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e0.141\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e\u003cp\u003e0.290238\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e126.313\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e6.7409\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e93.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e4.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e436.544\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e81.1319\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e0.141\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e\u003cp\u003e0.418368\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e518.923\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e21.7572\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e93.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e4.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e140.953\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.4318\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e0.141\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e\u003cp\u003e0.302927\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e518.923\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e6.7409\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e178.848\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e3.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e436.544\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.4318\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e0.141\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e\u003cp\u003e0.297765\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e126.313\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e21.7572\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e93.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e3.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e436.544\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.4318\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e148.723\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e\u003cp\u003e0.425328\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e518.923\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e21.7572\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e178.848\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e4.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e436.544\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e81.1319\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e148.723\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e\u003cp\u003e0.345428\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e126.313\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e6.7409\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e178.848\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e4.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e140.953\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.4318\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e148.723\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e\u003cp\u003e0.49692\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e518.923\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e6.7409\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e93.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e3.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e140.953\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e81.1319\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e148.723\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e\u003cp\u003e0.419777\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Results","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e4.1 Model establishment\u003c/h2\u003e\u003cp\u003ePareto optimality refers to an ideal state of resource allocation. In this experiment, a Pareto effect analysis was first conducted for each parameter factor, which is an analysis of the degree to which each parameter factor optimizes the final output. The results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe chart features the effect analysis of the crystallizer underflow concentration on the horizontal axis. The vertical axis represents the following independent parameters: Hourly Ore Throughput (T/h), KCl Content in Raw Ore, Hourly Flow Rate of Blended Mother Liquor (m\u0026sup3;/h), KCl Content in the Liquid Phase of Crystallizer Underflow, Volumetric Flow Rate of Crystallizer Underflow (m\u0026sup3;/h), Crystallizer Mist Water Flow Rate (m\u0026sup3;/h), and Crystallizer Fresh Water Input (m\u0026sup3;/h). A two-sided confidence interval was applied with a significance level of α\u0026thinsp;=\u0026thinsp;0.05.\u003c/p\u003e\u003cp\u003eThe analysis indicates that crystallizer fresh water input has the greatest effect on the dependent variable. The influences of the hourly Ore Throughput and KCl content in the Raw Ore are similar in magnitude, whereas the effects of the remaining factors are relatively minor. In response to these findings, a mixed-effects model incorporating these three key factors was established as a reference to increase modeling accuracy.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e4.2 Three-factor Mixed Effects Model\u003c/h2\u003e\u003cp\u003eThe hourly ore throughput (T/h), KCl content in raw ore, hourly flow rate of blended mother liquor (m\u0026sup3;/h), KCl content in the liquid phase of crystallizer underflow, volumetric flow rate of crystallizer underflow (m\u0026sup3;/h), crystallizer mist water flow rate (m\u0026sup3;/h), and crystallizer fresh water input (m\u0026sup3;/h) are denoted by the letters A to G, respectively, while the crystallizer underflow concentration is designated Y for subsequent computational convenience.\u003c/p\u003e\u003cp\u003eA mixed-effects model was established for three factors: crystallizer fresh water input, hourly ore throughput, and KCl content in raw ore. The corresponding error analysis results are presented in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eModel error analysis Generally, the p value represents the probability of obtaining the observed results, or more extreme ones, assuming that the null hypothesis is true. If the p value is less than the selected significance level (α\u0026thinsp;=\u0026thinsp;0.05), the null hypothesis is rejected. The Z value measures the number of standard deviations by which a sample mean deviates from the population mean. The coefficients for the overall model are presented in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e\u003cp\u003eVariance\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGroup\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eVariable\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eProportion\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eZ\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eP\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.001893\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e20.53%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.003110\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.608757\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.271\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eB\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.001959\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e21.24%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.003203\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.611659\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.270\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eG\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.004168\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e45.19%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.006323\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.659153\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.255\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eError\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.001203\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e13.04%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.000851\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.414214\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.079\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTotal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.009223\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e\u003cp\u003e\u0026minus;2Log=\u0026minus;18.414135\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThree-factor mixed effects model\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e\u003cp\u003eCoefficient\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGroup\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCoefficient\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eFree degree\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eT\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eP\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCon\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.374594\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.064502\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.31\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e5.807491\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.020\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhen the P value is less than or equal to the alpha (α) value, the differences between some of the means are considered statistically significant. On the basis of the results, since the P value is less than the significance level of 0.05, we conclude that the model is unacceptable.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003e4.3 Overall Model\u003c/h2\u003e\u003cp\u003eA model for 7 parameters was constructed, and variance analysis was performed on the model.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eAnalysis of variance\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e\u003cp\u003eVariance Analysis\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGroup\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFree degree\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAdj SS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eAdj MS\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModel\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.040501\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.005786\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLinearity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.040501\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.005786\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.008775\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.008775\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eB\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.009039\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.009039\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.002314\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.002314\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.002130\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.002130\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eE\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.000066\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.000066\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.000302\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.000302\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eG\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.017875\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.017875\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eError\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTotal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.040501\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eAdj MS\u0026thinsp;=\u0026thinsp;Adj SS/Degrees of Freedom, which is termed the Adjusted Mean Square. Adj SS, the adjusted sum of squares, represents the total sum of squares. It is the sum of the sum of squares for the model and the sum of squares for error, thereby quantifying the total variation in the data. Since the corresponding P values for both are below the significance level of 0.05, the results are considered acceptable.\u003c/p\u003e\u003cp\u003eThrough calculation, the final data model is derived as follows:\u003c/p\u003e\u003cp\u003e\u003cem\u003eY\u0026thinsp;=\u0026thinsp;0.4854-0.000169*A-0.004477*B-0.000398*C\u0026thinsp;+\u0026thinsp;0.01886*D-0.000019*E-0.000152*F\u0026thinsp;+\u0026thinsp;0.04727*G\u003c/em\u003e\u003c/p\u003e\u003cp\u003eSubstituting the parameter names yields the complete model:\u003c/p\u003e\u003cp\u003e\u003cem\u003eCrystallizer Underflow Concentration\u0026thinsp;=\u0026thinsp;0.4854\u0026ndash;0.000169 \u0026times; Hourly Ore Throughput \u0026minus;\u0026thinsp;0.004477 \u0026times; KCl Content in Raw Ore \u0026minus;\u0026thinsp;0.000398 \u0026times; Hourly Flow Rate of Blended Mother Liquor\u0026thinsp;+\u0026thinsp;0.01886 \u0026times; KCl Content in Liquid Phase of Crystallizer Underflow \u0026minus;\u0026thinsp;0.000019 \u0026times; Volumetric Flow Rate of Crystallizer Underflow \u0026minus;\u0026thinsp;0.000152 \u0026times; Crystallizer Mist Water Flow Rate\u0026thinsp;+\u0026thinsp;0.04727 \u0026times; Crystallizer Fresh Water Input\u003c/em\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003e4.4 Model Validation\u003c/h2\u003e\u003cp\u003eThe overall model was validated via 23 sets of valid data that were withheld from the model development process. Following the calculation of the results, error analysis was performed between the computed crystallizer underflow concentration data and the original measured data. This analysis included an evaluation of the root mean square error (RMSE) and the coefficient of determination (R\u0026sup2;). The results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv id=\"Sec16\" class=\"Section3\"\u003e\u003ch2\u003e4.4.1 RMSE analysis\u003c/h2\u003e\u003cp\u003eRMSE =​\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sqrt{\\text{1/}\\text{n}\\text{\u0026lowast;}\\sum\\:_{\\text{i}\\text{=1}}^{\\text{n}}\\text{（}{\\text{y}}_{\\text{i}}\\text{\u0026minus;}{\\text{y}{\\prime\\:}}_{\\text{i}}\\text{)^2}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003en represents the number of data points, y\u003csub\u003ei\u003c/sub\u003e is the data point in the original dataset, and ŷ\u003csub\u003ei\u003c/sub\u003e is the corresponding data point in the compared dataset. The calculated RMSE value is 0.014. A smaller RMSE indicates a better fit between the formula and the original data. This result demonstrates a good level of fit for the formula.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec17\" class=\"Section3\"\u003e\u003ch2\u003e4.4.2 R^2 Analysis\u003c/h2\u003e\u003cp\u003eR^2 = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{\\text{i}\\text{=1}}\\text{(}{\\text{y}}_{\\text{i}}\\text{\u0026minus;}{\\stackrel{\\text{ˇ}}{\\text{y}}}_{}\\)\u003c/span\u003e\u003c/span\u003e)(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{y}{\\prime\\:}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e-\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{\\text{ˇ}}{\\text{y}{\\prime\\:}}}_{}\\)\u003c/span\u003e\u003c/span\u003e)/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sqrt{\\sum\\:_{\\text{i}\\text{=1}}\\text{(}{\\text{y}}_{\\text{i}}\\text{\u0026minus;}{\\stackrel{\\text{ˇ}}{\\text{y}}}_{}\\text{)^2\u0026lowast;}\\sum\\:_{\\text{i=1}}\\text{(}{\\text{y}{\\prime\\:}}_{\\text{i}}\\text{\u0026minus;}{\\stackrel{\\text{ˇ}}{\\text{y}{\\prime\\:}}}_{}\\text{)}\\text{^2}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003eIn the formula, y\u003csub\u003ei\u003c/sub\u003e is the data point in the original dataset, ŷ\u003csub\u003ei\u003c/sub\u003e is the corresponding data point in the compared dataset,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{\\text{ˇ}}{\\text{y}}}_{}\\)\u003c/span\u003e\u003c/span\u003e is the mean of the original dataset, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{\\text{ˇ}}{\\text{y}{\\prime\\:}}}_{}\\)\u003c/span\u003e\u003c/span\u003e is the mean of the compared dataset.\u003c/p\u003e\u003cp\u003eR\u0026sup2; is used to evaluate the correlation between the formula-calculated data and the original data. A value of R\u0026sup2; closer to 1 indicates a better fit of the formula. The calculated result is 0.7443, which demonstrates a good level of fit for the formula.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"5. Discussion","content":"\u003cp\u003eOn the basis of actual production data from a potash fertilizer manufacturing site, this study utilized the DOE methodology to perform an optimization analysis of key parameters in the crystallizer treatment process. Through preliminary data screening, correlation analysis, and experimental design, seven key parameters were identified, including the hourly ore throughput (T/h), the KCl content in the raw ore, the hourly flow rate of the blended mother liquor (m\u0026sup3;/h), the KCl content in the liquid phase of the crystallizer underflow, the volumetric flow rate of the crystallizer underflow (m\u0026sup3;/h), the crystallizer mist water flow rate (m\u0026sup3;/h), and the crystallizer freshwater input rate (m\u0026sup3;/h). A systematic factorial design experiment was subsequently conducted for these parameters via Minitab 18 software, followed by an in-depth analysis of the experimental results.\u003c/p\u003e\u003cp\u003ePareto analysis revealed that the Crystallizer Freshwater Input has the most significant effect on the crystallizer underflow concentration. This finding underscores the critical importance of precise control over freshwater addition in enhancing the production efficiency and quality of potash fertilizer. Furthermore, the effects of Hourly Ore Throughput and the KCl Content in Raw Ore were found to be comparable in magnitude and significant, indicating that these parameters likewise play crucial roles in maintaining production stability and product quality.\u003c/p\u003e\u003cp\u003eA tentative mixed-effects model incorporating the three most influential parameters was developed. However, the analysis of variance (ANOVA) results for this model showed a P value greater than the significance level of 0.05, indicating that the model was not statistically significant at the current threshold.\u003c/p\u003e\u003cp\u003eThrough further comprehensive model analysis, a mathematical model incorporating all seven parameters was derived to predict the crystallizer underflow concentration. The ANOVA results demonstrated that both the total sum of squares and the error sum of squares were associated with P values below the 0.05 significance level, confirming the statistical reliability of the model. The model equation is as follows:\u003c/p\u003e\u003cp\u003e\u003cem\u003eCrystallizer Underflow Concentration\u0026thinsp;=\u0026thinsp;0.4854\u0026ndash;0.000169 \u0026times; Hourly Ore Throughput \u0026minus;\u0026thinsp;0.004477 \u0026times; KCl Content in Raw Ore \u0026minus;\u0026thinsp;0.000398 \u0026times; Hourly Flow Rate of Blended Mother Liquor\u0026thinsp;+\u0026thinsp;0.01886 \u0026times; KCl Content in Liquid Phase of Crystallizer Underflow \u0026minus;\u0026thinsp;0.000019 \u0026times; Volumetric Flow Rate of Crystallizer Underflow \u0026minus;\u0026thinsp;0.000152 \u0026times; Crystallizer Mist Water Flow Rate\u0026thinsp;+\u0026thinsp;0.04727 \u0026times; Crystallizer Fresh Water Input\u003c/em\u003e\u003c/p\u003e\u003cp\u003eThis model effectively captures the influence of various parameters on the crystallizer underflow concentration during production, providing a scientific theoretical basis for process optimization. It can be used not only to predict the crystallizer underflow concentration but also to simulate the crystallization performance under different production conditions by adjusting the parameter values within the model, thereby identifying the optimal combination of production parameters. Furthermore, the model can be employed for real-time monitoring of changes in key process parameters, helping to ensure operational stability and consistent product quality.\u003c/p\u003e\u003cp\u003eThe main contributions and innovations of this paper include the following:\u003c/p\u003e\u003cp\u003eIdentification of Key Parameters: Through effective screening of production data and correlation analysis, seven key parameters influencing the crystallizer underflow concentration were successfully identified.\u003c/p\u003e\u003cp\u003ePareto analysis: Pareto analysis demonstrated that the fresh water input of the crystallizer has the most significant effect on the underflow concentration, with the hourly ore throughput and the KCl content in the raw ore also highly influential.\u003c/p\u003e\u003cp\u003eModel development and optimization: On the basis of the DOE experimental design, a mathematical model incorporating all seven parameters was established to predict the crystallizer underflow concentration. The model's validity was confirmed via analysis of variance (ANOVA).\u003c/p\u003e\u003cp\u003eSystematic analytical methodology: This research provides a systematic and comprehensive analysis and optimization of multiple key parameters in the potash fertilizer production crystallizer process. The methodology, involving screening and correlation analysis, enables relatively accurate prediction of the crystallizer underflow concentration.\u003c/p\u003e\u003cp\u003eInvestigation of Multifactor Interactions: This study considered not only the individual effects of single parameters on the crystallizer underflow concentration but also the interactions between multiple parameters, offering valuable insights for optimizing complex production systems.\u003c/p\u003e\u003cp\u003eOn the basis of the findings of this study, the following production optimization recommendations are proposed:\u003c/p\u003e\u003cp\u003eOptimize the Crystallizer Freshwater Input: Given that the fresh water input has the most significant effect on the crystallizer underflow concentration, precise control of this parameter should be enhanced to reduce variability and improve product quality.\u003c/p\u003e\u003cp\u003eMonitoring the Hourly Ore Throughput and Raw Ore KCl Contents: Although the influence of these two parameters is secondary to the freshwater input, their stability is equally crucial for smooth process operation. They should be regularly monitored and adjusted to remain within optimal ranges.\u003c/p\u003e\u003cp\u003eTo comprehensively consider other parameters, while the remaining parameters have a lesser individual impact on the underflow concentration, their variations should still be fully considered in actual production to maximize overall production efficiency.\u003c/p\u003e\u003cp\u003eImplementing continuous monitoring and feedback: Establish a robust production monitoring system for real-time tracking and logging of all key parameters. The process parameters should be promptly adjusted on the basis of the monitoring results to ensure process stability and controllable product quality.\u003c/p\u003e\u003cp\u003eGiven the complexity and diversity of potash fertilizer production processes, while this study has achieved certain results, further in-depth research and improvement are necessary. Future work involving more experimentation and data analysis can further optimize the production model and enhance efficiency:\u003c/p\u003e\u003cp\u003eModel Refinement and Validation: Future research should focus on increasing the sample size to reduce the impact of data variability on the model outcomes and incorporate more potential influencing factors to improve the model's accuracy and reliability. Concurrently, the model requires validation within actual production environments to ensure its effectiveness in practical applications.\u003c/p\u003e\u003cp\u003eResearch on Green Production Processes: As environmental regulations become increasingly stringent, future studies should also address environmental concerns in potash production. This can be achieved by optimizing production processes and introducing green production technologies to reduce energy consumption and environmental pollution, ultimately achieving sustainable development.\u003c/p\u003e\u003cp\u003eComprehensive Optimization Research: Beyond the crystallizer treatment process, the DOE methodology can be applied to other stages of potash production, such as raw material pretreatment and evaporation crystallization, to achieve integrated optimization of the entire production chain.\u003c/p\u003e\u003cp\u003eIn summary, this study provides foundational support for the optimization of the potash production process. Future research will continue to explore areas such as model refinement and the development of intelligent control systems.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor contributions statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAuthor 1 (First Author): Ye Sun, conceptualization, methodology, software, investigation, formal analysis, writing - original draft, corresponding author;\u003c/p\u003e\n\u003cp\u003eAuthor 2: Ziheng Ma, Data Curation, Writing - Review \u0026amp; Editing, Visualization, Investigation;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll\u0026nbsp;the\u0026nbsp;authors disclosed no relevant relationships.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding Source Declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eA\u003c/strong\u003e\u003cstrong\u003evailability\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eS\u003c/strong\u003e\u003cstrong\u003etatement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data generated or analysed during this study are included in this published article [and its supplementary information files].\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eLi, Y., Ma, Z. \u0026amp; Song, X. New Advances in the Development of Potassium Resources from Qinghai Chloride-Type Salt Lakes and Suggestions for Industrial Development. \u003cem\u003eInorg. Chemicals Ind.\u003c/em\u003e (\u003cb\u003e08\u003c/b\u003e), (2023).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHe, F. \u0026amp; Gao, C. Application of Common Salt Lake Potassium Chloride Production Processes. \u003cem\u003eChem. Manage.\u003c/em\u003e (\u003cb\u003e06\u003c/b\u003e), (2023).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCheng, P. Study on Process Control of Potassium Chloride Production by Reverse Flotation-Cold Crystallization. \u003cem\u003eChina Petroleum Chem. Standard Qual.\u003c/em\u003e (\u003cb\u003e24\u003c/b\u003e), (2022).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLei, B. \u0026amp; Chen, M. Comprehensive Energy Consumption Analysis and Countermeasures for Potassium Chloride Production. \u003cem\u003eSalt Sci. Chem. Ind.\u003c/em\u003e (\u003cb\u003e08\u003c/b\u003e), (2022).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGuo, Y., Liu, Q. \u0026amp; Li, X. Research on Optimization of Energy-Saving Equipment in Hot Leaching-Crystallization Potassium Chloride Production Process. \u003cem\u003eChem. Manage.\u003c/em\u003e (\u003cb\u003e36\u003c/b\u003e), (2021).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLi, Y., Wang, N. \u0026amp; Liu, X. Equipment and Process for Potassium Chloride Production Crystallization. \u003cem\u003eChem. Manage.\u003c/em\u003e (\u003cb\u003e11\u003c/b\u003e), (2021).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang, Y. \u0026amp; Yang, M. Study on Process Control of Potassium Chloride Production by Reverse Flotation-Cold Crystallization. \u003cem\u003eChem. Eng. Des. Commun.\u003c/em\u003e \u003cb\u003e50\u003c/b\u003e (08), 7\u0026ndash;9 (2024).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHuo, Y. et al. Control of Water Addition in Cold Crystallization Step of Potassium Chloride by Reverse Flotation-Cold Crystallization Method. \u003cem\u003eSalt Sci. Chem. Ind.\u003c/em\u003e \u003cb\u003e52\u003c/b\u003e (12), 26\u0026ndash;30 (2023).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePatel, H., M\u0026uuml;ller, F., Maiti, P. \u0026amp; Maiti, S. Economic evaluation of solar-driven thermochemical conversion of empty cotton boll biomass to syngas and potassic fertilizer. \u003cem\u003eEnergy. Conv. Manag.\u003c/em\u003e \u003cb\u003e209\u003c/b\u003e, 112631 (2020).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBasystiuk, Y. I. \u0026amp; Kostiv, I. Y. Getting Hydrated Magnesium Chloride from Magnesium Chloride Solutions of Potassium Sulfate Fertilizers Production. \u003cem\u003eJ. Chem. Eng. Process. Technol.\u003c/em\u003e \u003cb\u003e7\u003c/b\u003e (2), 1\u0026ndash;4 (2016).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang, L., Xu, Y., Chen, H. \u0026amp; Song, X. New insights into octadecylamine-monoacid selective adsorption on KCl/NaCl surface: Experimental and molecular dynamic simulation. \u003cem\u003eAppl. Surf. Sci.\u003c/em\u003e (2021).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhong, A. et al. Atomic insights into flotation separation of KCl and NaCl from a new viewpoint of hydration layer: A molecular dynamic study. Colloids and Surfaces A: Physicochemical and Engineering Aspects (2020).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHuang, Z. et al. Evaluation of a novel morpholine-typed Gemini surfactant as the collector for the reverse flotation separation of halite from carnal lite ore. \u003cem\u003eJ. Mol. Liq.\u003c/em\u003e (2020).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang, P. L. K., Hsiao, C. C. \u0026amp; Ho, K. C. Y. C. Optimization of Nd:YAG laser welding onto magnesium alloy via Taguchi analysis. \u003cem\u003eOpt. Laser Technol.\u003c/em\u003e (\u003cb\u003e04\u003c/b\u003e), (2014).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang, X. et al. Technological Progress in Potassium Extraction from Qinghai Salt Lakes and the Development of China's Potash Fertilizer Industry. \u003cem\u003eChem. Minerals Process.\u003c/em\u003e (\u003cb\u003e11\u003c/b\u003e), (2017).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMa, F. \u003cem\u003eSix Sigma Management Statistical Guide\u003c/em\u003e (Renmin University of China, 2018).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKempe, M. D., Jorgensen, G. J., Terwilliger, K. M., McMahon, T. J. \u0026amp; Kennedy, C. E. \u0026amp; Borek T. T. Acetic acid production and glass transition concerns with ethylene-vinyl acetate used in photovoltaic devices. \u003cem\u003eSol. Energy Mater. Sol. Cells\u003c/em\u003e (\u003cb\u003e04\u003c/b\u003e), (2016).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMin, Y. \u003cem\u003eDesign of Experiments (DOE) Application Guide\u003c/em\u003e (China Machine, 2011).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTan, S. Insights from Domestic and Foreign Practices in Comprehensive Development and Utilization of Salt Lake Resources for Qinghai Salt Lake Resources. \u003cem\u003eSalt Sci. Chem. Ind.\u003c/em\u003e (\u003cb\u003e08\u003c/b\u003e), (2017).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang, H. \u003cem\u003eMultscale Coupling Model and Optimization Study on the Preparation Process of Potassium Chloride and Magnesium Chloride Hydrates\u003c/em\u003e (Tianjin University of Science and Technology, 2014).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Potassium fertilizer production, DOE experimental design, crystallizer bottom flow concentration","lastPublishedDoi":"10.21203/rs.3.rs-7954338/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7954338/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study aims to optimize the crystallizer operation in a potash production facility at Qinghai Salt Lake by applying the DOE methodology in conjunction with specific experimental data. The objective is to increase production efficiency and product quality. The analysis begins by examining the current state of potash production, highlighting the industry's challenges in improving efficiency, reducing costs, and minimizing environmental impact. Multiple key parameters of the crystallizer process were investigated, including temperature, pressure, agitation speed, and raw material composition.\u003c/p\u003e\u003cp\u003eThrough multiple rounds of DOE experiments, the critical factors significantly influencing crystallization performance were identified. A corresponding mathematical model was developed and validated. On the basis of this model, optimized operating conditions were proposed to increase the potash crystallization yield while reducing energy consumption and production costs. The advantages and limitations of employing the DOE approach in this context are thoroughly discussed, along with potential directions for future research.\u003c/p\u003e","manuscriptTitle":"Design of Experiments: Model Development and Optimization of the Cold Crystallization Process in Potash Production","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-19 09:54:46","doi":"10.21203/rs.3.rs-7954338/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b3c6ccd4-5819-4ed2-bb3e-c71d0d3a239f","owner":[],"postedDate":"November 19th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":57739314,"name":"Physical sciences/Energy science and technology"},{"id":57739315,"name":"Physical sciences/Engineering"},{"id":57739316,"name":"Earth and environmental sciences/Environmental sciences"},{"id":57739317,"name":"Physical sciences/Materials science"}],"tags":[],"updatedAt":"2026-04-21T02:54:27+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-19 09:54:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7954338","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7954338","identity":"rs-7954338","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}