The Optimized Synthesis of Barium Sulfate: A Scalable and Sustainable Laboratory Approach Using D-Optimal Design

Abstract

This study introduces a controlled laboratory-scale method for synthesizing barium sulfate, with promising potential for industrial scalability to meet increasing demand for quality and sustainable production. Statistical tools—specifically, design of experiments (DOE) and the D-optimal methodology via DX12.0.3.0 software—were employed to determine optimal reaction parameters. The synthesis process involved the precise control of barium chloride and sulfate concentrations, feed rate, and temperature to ensure the production of barium sulfate. Under optimized conditions (BaCl₂ = 1.5 M, SO₄²⁻ = 0.41 M, flow rate = 2.53 mL/min, temperature = 20.03 °C), a yield of 9.20 g of barium sulfate with a density of 4.25 g/cm³ was achieved. The analysis confirmed the purity of the product, validating its suitability for demanding industrial applications. This approach not only improves product quality but also minimizes waste and reduces operational costs, offering a sustainable and scalable solution for barium sulfate production. These findings mark a meaningful step forward in mineral processing and purification technologies.

1. Introduction

Barite (BaSO₄) has transitioned from being a low-value mineral to a resource of strategic significance across various industries, especially in the energy sector. Its unique attributes, including high density and chemical inertness, render it essential for oil exploration and drilling. Notably, nearly 90% of global barite consumption is attributed to its function as a weighting agent in drilling fluids, which are critical for stabilizing wellbores and managing formation pressures to ensure operational safety and efficiency [1,2,3,4,5,6]. The exceptional density and minimal solubility of barite make it ideally suited for drilling applications, as it effectively counters formation fluid pressures, thereby reducing blowout risks and enhancing stability. Beyond oil and gas, barite’s versatility has facilitated its adoption across diverse industries. Its physical and chemical properties are leveraged in pigment production, where its high refractive index and chemical inertness contribute to superior optical and functional traits [7,8]. As a critical component in drilling mud, barite’s characteristics—being clean, soft, inert, and economically viable—are further amplified by its specific gravity exceeding 4 g/cm³, making it an effective weighting agent [9,10]. Its functions extend to cooling and lubricating drill bits, lining well casings, and facilitating drilling fluid transport, concurrently controlling abnormal formation pressures [11]. Natural barium sulfate with a purity of 90%–95% and minimal iron oxide contamination (<1%) is extensively utilized in manufacturing high-quality white pigments and as a viscosity modifier in paints. In contrast, synthetic barium sulfate, commonly known as blanc fixe, is produced through the precipitation of pure barium sulfate from a chemical reaction between sodium sulfate (Glauber’s salt) and barium sulfide [12,13,14,15]. In pharmaceuticals, although overall industrial mineral consumption is lower, barite’s economic value is notable when processed to meet rigorous standards, requiring purity levels exceeding 97.5% [16,17,18]. Barium sulfate serves a crucial role as a contrast agent in X-ray and CT imaging, enhancing diagnostic image quality by improving the visibility of internal structures [19,20,21]. However, care is necessary for patients with certain conditions due to the potential adverse effects if used improperly [22,23]. In cases where barite contains witherite, the resulting solution can become toxic, potentially causing kidney dysfunction or paralysis. Therefore, the use of barium sulfate in medical procedures should always adhere to the guidance of a qualified healthcare professional [24,25,26].

At the turn of the 19th and early 20th centuries, several materials were tested as contrast agents for X-ray imaging. Initially, heavy metal salts and oxides were suggested for this purpose. The first material employed was bismuth nitrogen compounds, which, however, caused significant toxicity. Subsequently, bismuth carbonate and high-atomic-number metal oxides, such as thorium oxides, were utilized. Due to the hazardous nature of these substances, barite (barium sulfate) emerged as a safer alternative. Nevertheless, the use of barite was not devoid of complications, as impurities often resulted in toxic effects [27,28,29]. In 1911, the Mallinckrodt Chemical Company introduced a method called the “black ash process” to purify barite and convert it into soluble barium salts [30]. By 1913, this method was industrially implemented, marking a significant advancement in barite refinement. The black ash process facilitated the removal of impurities, rendering barite a safer and more efficient material for diverse applications [31,32,33]. In 1930, Henry Farr proposed an alternative process using calcium chloride instead of oil and gas to convert barium sulfate. This method involved purifying barite and transforming it into a complex salt, followed by hydrolysis of the complex salt, which led to the precipitation of barium sulfate. Other salts, such as potassium chloride, potassium nitrate, and chromium or iron sulfates, could also form complex salts with barite. This method produced fine precipitates, effectively separating impurities like iron oxides and siliceous materials from barite [34,35,36]. Later, in 1936, Norris and colleagues expanded on Farr’s invention and succeeded in extracting soluble salts from both barium and strontium sulfates. The reaction demonstrated optimal efficiency when equimolar ratios of barium sulfate and calcium chloride (containing 3–5 parts water) were subjected to intense heat for a brief period, resulting in their fusion. The resulting product was cooled using a methanol–ethylene glycol mixture, yielding barium chloride with a purity of 95% or higher [37,38,39,40,41]. Tasbolatovna reviewed various methods for producing high-purity barium sulfate. The study highlighted common impurities in the synthesis process, including sodium and ammonium chlorides, as well as sulfur-based compounds such as sulfur chloride or SO₂. The use of barium hydroxide was found to effectively reduce sulfide impurities. In one method, sulfuric acid and hydrochloric acid were employed for washing barite, with high-purity barite being essential for optimal results. This process upgraded barite with an initial purity of 95%–98% to a final grade of 99% purity. Additionally, barite purification was achieved by dissolving it in molten salt mixtures of sodium chloride and calcium chloride. After separating the solid and molten phases and washing with water, pure barium sulfate was obtained. This high-purity barium sulfate has proven applications in industries such as battery production and papermaking [42].

Recent studies emphasize the growing need for sustainable mineral processing routes to produce high-purity compounds with minimal environmental impact [43]. These applications require not only high chemical purity but also narrow particle size distribution and high density, which are difficult to achieve using conventional techniques. Our approach aligns with these modern standards by applying statistically optimized synthesis methods to produce BaSO₄ with over 96% purity, reducing reagent waste. In addition to achieving high purity and yield, the proposed synthesis method demonstrates improved environmental sustainability. The use of a statistically optimized D-optimal design allowed for minimal reagent consumption—specifically reducing excess use of barium chloride and sulfuric acid [44,45,46]. As the reaction proceeds via a simple precipitation mechanism under ambient temperature and pressure, it eliminates the need for high-energy input or hazardous catalysts. Furthermore, no secondary or toxic by-products are formed during the process, and the resulting supernatant is non-corrosive and can be treated using standard neutralization protocols, making the approach compliant with green chemistry principles. Compared to conventional high-temperature or multi-step methods, our process significantly lowers the environmental footprint and aligns with recent efforts to develop cleaner mineral synthesis techniques [47,48].

In this study, we introduce a streamlined and environmentally conscious synthesis method for producing barium sulfate. Traditional synthesis routes often require extensive material input and generate unnecessary waste. In contrast, our methodology leverages the D-optimal design approach within a Design of Experiments (DOE) framework to systematically optimize key variables—including reactant concentrations, flow rate, and reaction temperature. Implemented through DX12 software, this statistical strategy allowed for efficient identification of ideal process conditions using fewer experimental runs [49,50,51]. By refining these parameters, we achieved consistent product quality with improved mass yield and density, while minimizing chemical usage and operational overhead. This integrated approach not only enhances scalability and reproducibility but also aligns with sustainable processing practices by reducing environmental impact—addressing both performance and ecological considerations in industrial mineral synthesis.

2. Materials and Methods

2.1. Production of Barium Sulfate

Barium carbonate (BaCO₃), hydrochloric acid (HCl) and sulfuric acid (H₂SO₄) were used. All reagents used in the experiments are industrial grade purity reagents. Barium chloride (BaCl₂) was synthesized by reacting barium carbonate (BaCO₃) with hydrochloric acid (HCl) according to the following reaction (Equation (1)):

$$2\mathrm{H}\mathrm{C}\mathrm{l}\left(\mathrm{a}\mathrm{q}\right)+\mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{O}}_3\left(\mathrm{s}\right)\to \mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{l}}_2\left(\mathrm{a}\mathrm{q}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{a}\mathrm{q}\right)+\mathrm{C}{\mathrm{O}}_2\left(\mathrm{g}\right)$$

(1)

Hydrochloric acid was added to an acid-resistant vessel, followed by the gradual introduction of barium carbonate powder while continuously stirring with a mechanical stirrer. This ensured an enhanced reaction rate and prevented premature precipitation of barium carbonate. The reaction proceeded until the pH was adjusted neutrality, at which point a portion of barium carbonate remained as a precipitate. Once complete sedimentation was achieved, the remaining solution was carefully separated for further processing.

To prepare 1 L of 1 M H₂SO₄, 55 mL of concentrated sulfuric acid was carefully added to approximately 800 mL of distilled water in a fume hood with continuous stirring, and then the solution was diluted to a final volume of 1 L using a volumetric flask. During the experimental procedure, varying concentrations of barium chloride solution were reacted with the prepared H₂SO₄ under magnetic stirring. This reaction resulted in the formation of barium sulfate (BaSO₄) as a precipitate and hydrochloric acid (HCl) as a byproduct, as represented by the following chemical equation (Equation (2)):

$$\mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{l}}_2\left(\mathrm{a}\mathrm{q}\right)+{\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4\left(\mathrm{a}\mathrm{q}\right)\to \mathrm{B}\mathrm{a}\mathrm{S}{\mathrm{O}}_4\left(\mathrm{s}\right)+2\mathrm{H}\mathrm{C}\mathrm{l}\left(\mathrm{a}\mathrm{q}\right)$$

(2)

The density of the barium sulfate samples was determined using a standard pycnometer method in accordance with ASTM D2330 [52]. A pycnometer of known volume (25 mL) was used for the measurement. Approximately 5–15 g of oven-dried sample was accurately weighed and placed into the pycnometer. Deionized water was then added to fill the pycnometer, ensuring that no air bubbles remained trapped. Then, the mass of the filled pycnometer was recorded. The density of the dry sample ($\rho$ₛ) was calculated using the following equation (Equation (3)):

$${\rho }_{\mathrm{s}}={\displaystyle \frac{{\mathrm{m}}_{\mathrm{s}}\times {\rho }_{\mathrm{w}}}{\left({\mathrm{m}}_{\mathrm{p}\mathrm{w}}-{\mathrm{m}}_{\mathrm{p}}\right)-({\mathrm{m}}_{\mathrm{p}\mathrm{s}\mathrm{w}}-{\mathrm{m}}_{\mathrm{p}}-{\mathrm{m}}_{\mathrm{s}})}}$$

(3)

where

mₛ is the mass of the dry sample,

mₚ is the mass of the empty pycnometer,

m_pw is the mass of the pycnometer filled with water,

m_psw is the mass of the pycnometer filled with sample and water,

$\rho$ₚ is the density of the water at the measurement temperature.

Each measurement was performed in triplicate, and the average value was reported to ensure accuracy and repeatability.

2.2. Experimental Design

The following sections describe the experimental design and synthesis methodology used to produce barium sulfate via a synthetic approach. Initial experiments revealed a direct correlation between the barium concentration and the density of the resulting barium sulfate. Consequently, the density of the synthesized barium sulfate was selected as a key response variable for the optimization study. To efficiently determine the optimal synthesis conditions while minimizing the number of experimental trials, the design of experiments (DOE) methodology was applied. This statistical approach allows for the evaluation of both individual parameters and their interactions on the synthesis process [53,54,55]. The experimental design was developed using DX12 software, employing the D-optimal design strategy to guide the optimization.

The input parameters were defined as the barium chloride concentrations, sulfate concentrations, feed rate, and temperature. The output parameters were the mass of the produced barium sulfate (in grams) and its density. The minimum and maximum concentrations of barium chloride and sulfuric acid were set between 0.35 M and 1.5 M, based on the solubility product constants (K_SP) of the chemical compounds, the relevant literature, and experimental constraints. The concentration range was considered to be from 0.35 to 1.5 M. Increasing the concentration beyond this value would cause high acidity of the medium and failure of the reaction to complete. The feed rate was determined to range from 2.5 to 20 mL/min, considering the limitations of the laboratory burette. The solution temperature range was specified as 20–80 °C. The input parameter ranges used in the software, based on the results of preliminary experiments, are provided in

Table 1. The range of the input variables used in the experimental design.

Parameter	Type	Minimum Value	Maximum Value	Mean
Barium chloride concentration (mol/L)	A	0.35	1.5	0.919
Sulfate concentration (mol/L)	B	0.35	1.5	0.904
Feed rate (mL/min)	C	2.5	20	10.617
Temperature (°C)	D	20	80	53.776

. Additionally, the experimental design by DX12 software is detailed in

Table 2. Experimental design for process optimization.

Experiment No.	Barium Chloride Concentration (M)	Sodium Sulfate Concentration (M)	Flow Rate (mL/min)	Temperature (°C)
1	1.5000	0.4398	20.00	72.05
2	0.3500	1.5000	2.50	20.00
3	1.3742	0.7143	11.51	46.57
4	0.3500	0.3500	2.50	80.00
5	0.3500	0.9625	20.00	42.49
6	1.5000	1.5000	20.00	80.00
7	1.5000	1.5000	11.24	39.45
8	1.5000	0.8547	2.50	20.00
9	1.5000	0.8547	2.50	20.00
10	0.9634	0.3500	2.50	42.86
11	0.3500	1.4820	2.50	71.46
12	0.8551	1.5000	20.00	20.00
13	1.5000	0.3500	5.58	80.00
14	1.5000	1.5000	2.50	80.00
15	0.3500	0.3500	20.00	80.00
16	0.3500	1.5000	17.32	80.00
17	0.9191	0.9310	11.21	80.00
18	1.5000	1.5000	2.50	80.00
19	0.9250	0.9250	11.25	20.00
20	0.3500	0.3500	2.50	80.00
21	1.5000	0.3500	20.00	20.00
22	0.3500	0.3500	11.23	20.00
23	0.9483	1.1748	3.59	47.04
24	0.3500	0.9625	20.00	42.49
25	0.3500	0.3500	20.00	80.00

.

3. Results and Discussion

The product process optimization of barium sulfate was evaluated using DX12 software. In this regard, the key parameters, including barium chloride concentration, sulfate concentration, feed rate, and temperature, were studied.

3.1. Numerical Experimental Results

The input parameters considered were barium chloride concentration, sulfate concentration, feed rate, and temperature, while the output parameters were the mass of the produced barium sulfate and its density. The experimental results were analyzed using DX12 software. The regression equations for the mass of the produced barium sulfate and density are given as Equations (4) and (5), respectively (the models are expressed in terms of coded variables).

$$\begin{array}{ll}\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{s}=& 15.48+(4.91\times \mathrm{A})+(7.36\times \mathrm{B})+(-0.34\times \mathrm{C}+\left(-0.10\times \mathrm{D}\right)+\left(4.37\times \mathrm{A}\mathrm{B}\right)\\ & +\left(0.19\times \mathrm{A}\mathrm{D}\right)+\left(-0.16\times \mathrm{B}\mathrm{C}\right)+\left(0.23\times \mathrm{C}\mathrm{D}\right)+\left(-2.95\times {\mathrm{A}}^2\right)+(-1.87\times {\mathrm{B}}^2)\\ & +(-0.60\times {\mathrm{C}}^2)+(1.58\times {\mathrm{D}}^2)+(-1.06\times {\mathrm{A}}^2\mathrm{B})+(-1.60\times {\mathrm{A}}^2\mathrm{D})+(0.74\times \mathrm{A}{\mathrm{D}}^2)\\ & +(-1.79\times \mathrm{B}{\mathrm{C}}^2)+(2.45\times {\mathrm{C}}^2\mathrm{D})\end{array}$$

(4)

$$\begin{array}{ll}\mathrm{D}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}=& 3.90+\left(0.06\times \mathrm{A}\mathrm{ }\right)+\left(-0.07\times \mathrm{B}\right)+\left(-0.03\times \mathrm{C}\right)+\left(-0.04\times \mathrm{D}\right)+\left(-0.04\times \mathrm{A}\mathrm{B}\right)\\ & +(-0.004\times \mathrm{B}\mathrm{C})+(0.06\times \mathrm{B}\mathrm{D})+(0.02\times \mathrm{C}\mathrm{D})+(0.03\times {\mathrm{A}\mathrm{ }}^2)+(-0.05\times {\mathrm{B}}^2)\\ & +(-0.05\times \mathrm{B}\mathrm{C}\mathrm{D})\mathrm{ }+(0.04\times {\mathrm{B}}^2\mathrm{C})\end{array}$$

(5)

The statistical results of the developed models are presented in

Table 3. Statistical evaluation of model accuracy in predicting mass and density of synthesized barium sulfate.

Model	R2	Adjusted R2	Standard Deviation	Mean	Adequate Precision	Coefficient of Variation (%)
Mass (g)	1.00	0.99	12.86	12.86	247.33	0.78
Density (g/cm3)	0.82	0.64	0.083	3.88	7.80	2.16

. The value of the adequate precision component exceeds four, indicating a satisfactory level of accuracy [56,57]. Other parameters, such as the coefficient of determination (R²), also demonstrate the efficacy of these models in predicting the mass of the produced barium sulfate and density [58,59,60].

The data presented in

Table 4. Results of the analysis of variance (ANOVA) for the developed model on the mass of barium sulfate produced.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	1449.19	17	85.25	8458.53	<0.0001	significant
A	22.61	1	22.61	2243.47	<0.0001
B	22.61	1	22.61	2243.12	<0.0001
C	1.03	1	1.03	102.42	<0.0001
D	0.0200	1	0.0200	1.99	0.2013
AB	94.39	1	94.39	9365.88	<0.0001
AD	0.1983	1	0.1983	19.68	0.0030
BC	0.2080	1	0.2080	20.64	0.0027
CD	0.3143	1	0.3143	31.18	0.0008
A2	14.87	1	14.87	1475.61	<0.0001
B2	4.10	1	4.10	406.45	<0.0001
C2	0.3894	1	0.3894	38.64	0.0004
D2	4.84	1	4.84	480.01	<0.0001
A2B	0.8433	1	0.8433	83.68	<0.0001
A2D	1.36	1	1.36	135.19	<0.0001
AD2	0.3161	1	0.3161	31.37	0.0008
BC2	2.37	1	2.37	235.36	<0.0001
C2D	2.63	1	2.63	261.00	<0.0001
Residual	0.0705	7	0.0101
Lack of Fit	0.0055	2	0.0027	0.2113	0.8164	not significant
Pure Error	0.0650	5	0.0130
Cor Total	1449.26	24

show the results of the model for the mass of produced barium sulfate. The F-value of the model is 8458.53, which indicates that the model is statistically significant. The probability of obtaining an F-value this large due to random variation or noise is only 0.01%, affirming the robustness of the model. Furthermore, p-values less than 0.05 suggest that the corresponding model terms are statistically significant. In this context, the following terms are significant: A, B, C, AB, AD, BC, CD, A², B², C², D², A²B, A²D, AD², BC², and C²D. On the other hand, terms with p-values greater than 0.1 are considered not significant, implying that their contribution to the model is negligible. As presented in

Table 5. Results of the analysis of variance (ANOVA) for the developed model on the density of barium sulfate produced.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	0.3864	12	0.0322	4.59	0.0066	significant
A	0.0803	1	0.0803	11.43	0.0055
B	0.0633	1	0.0633	9.02	0.0110
C	0.0020	1	0.0020	0.2837	0.6040
D	0.0199	1	0.0199	2.83	0.1182
AB	0.0172	1	0.0172	2.45	0.1431
BC	0.0002	1	0.0002	0.0233	0.8812
BD	0.0425	1	0.0425	6.06	0.0300
CD	0.0026	1	0.0026	0.3659	0.5565
A2	0.0021	1	0.0021	0.2941	0.5975
B2	0.0074	1	0.0074	1.06	0.3243
BCD	0.0143	1	0.0143	2.03	0.1793
B2C	0.0032	1	0.0032	0.4532	0.5136
Residual	0.0842	12	0.0070
Lack of Fit	0.0510	7	0.0073	1.09	0.4772	not significant
Pure Error	0.0333	5	0.0067
Cor Total	0.4707	24

, the data correspond to the model of barium sulfate density. The F-value of 4.59 indicates that the model is statistically significant. This value suggests that there is only a 0.66% probability that such an F-value could arise due to random variation or noise, reinforcing the robustness of the model. Further analysis reveals that p-values less than 0.0500 denote statistically significant model terms. In this case, the model terms A, B, and BD are significant, confirming their relevance in predicting the barium sulfate density. Conversely, any model term with a p-value greater than 0.1000 is considered non-significant, and such terms do not contribute meaningfully to the model’s predictive capability. This statistical significance of the model terms and the low probability of noise-driven results underline the model’s strong predictive accuracy and reliability [61].

3.1.1. Mass of Barium Sulfate

Figure 1 displays the normal probability plot for the barium sulfate mass model, illustrating the distribution of residuals and the likelihood of each experimental outcome based on residual interpolation. The clustering of data points along the reference line indicates that the model accurately captures the relationship between sulfuric acid and barium chloride in barium sulfate production. This alignment suggests strong predictive capability and minimal deviation in error distribution. Figure 2 further supports this by comparing the actual mass of barium sulfate produced with the model’s predicted values. The data points lie closely along the line of identity, confirming the model’s robustness and reliability in predicting barium sulfate mass. Together, these plots validate the model’s effectiveness in representing the key dynamics of the synthesis process.

Figure 3 illustrates that with the increase in the concentrations of barium chloride and sulfuric acid, the mass of the produced barium sulfate rises correspondingly. However, an excessive concentration of sulfuric acid in the reaction environment inhibits the growth of barium sulfate crystals, leading to a reduction in the overall material production. The feed rate also impacts the mass of the produced material; specifically, an increase in the feed rate results in a lower mass of produced material. Temperature does not significantly influence this process.

Figure 4 showcases the influence of critical parameter interactions on the mass of produced barium sulfate. The response surface plots offer an in-depth visualization of how varying conditions impact the synthesis process. In Figure 4a, the effects of barium chloride and sulfate concentrations are analyzed. The data clearly indicate that simultaneously increasing the concentrations of these reactants significantly enhances the mass of barium sulfate produced, underscoring that higher reactant concentrations promote more efficient barium sulfate precipitation. Figure 4b illustrates the relationship between BaCl₂ concentration and temperature. The findings reveal that while an increase in BaCl₂ concentration markedly boosts production, the temperature, ranging from 20 °C to 80 °C, exerts a minimal influence on the mass. This observation suggests that within the examined range, temperature is not as crucial a parameter as reactant concentration. Figure 4c investigates the impact of sulfate concentration and flow rate. It becomes evident that reducing the flow rate leads to a notable increase in the mass of barium sulfate produced, even with slight variations in sulfate concentration. This indicates that lower flow rates extend the residence time, thereby enhancing precipitation efficiency. Figure 4c suggests that reducing the flow rate leads to increased mass production, likely because lower flow rates provide more time for the barium sulfate particles to nucleate and grow. This is particularly important in continuous flow reactors, where optimizing the residence time can lead to higher yields without the need for excessive increases in reactant concentrations. Figure 4d examines the interaction between temperature and flow rate. The analysis reveals that variations in flow rate have a more substantial impact on the mass of barium sulfate at lower temperatures. As temperatures rise, this effect lessens, highlighting a complex interaction where specific temperature ranges dampen the influence of flow rate on the precipitation process. In conclusion, the response surface methodology illustrated in Figure 4 emphasizes the critical role of optimizing reactant concentrations and flow rate to maximize the efficiency of barium sulfate production, while temperature assumes a more secondary role.

3.1.2. Density of Barium Sulfate

Figure 5 and Figure 6 present, respectively, the normal probability plot and the distribution of actual response values versus predicted values for the density model. The data in both of these plots align with the model’s predictions, further validating its accuracy and consistency.

Additionally, Figure 7 demonstrates that as the concentration of barium chloride increases, the density of barium sulfate rises. Conversely, increasing the concentration of sulfate and temperature results in a decrease in density. The feed rate does not have a significant effect on the density of the barium sulfate produced using sulfuric acid.

Figure 8 presents a series of response surface plots that illustrate the interactions between key parameters and their effect on the density of produced barium sulfate. These plots provide valuable insights into how variations in factors such as concentration, flow rate, and temperature influence the synthesis process and the resulting barium sulfate density. The slight increase in density with increasing concentrations of barium chloride and sulfate (as shown in Figure 8a) reflects the tendency for denser products to form under higher concentrations of reactants. This may be due to enhanced crystal growth and aggregation of particles, leading to a more compact structure. In industrial applications, higher density barium sulfate can be beneficial for certain applications, such as in drilling fluids, where product density is a critical parameter. Figure 8b explores the relationship between sulfate concentration and flow rate. The findings indicate that changes in flow rate have a relatively minor effect on the density of barium sulfate, particularly when the sulfate concentration is held constant. This suggests that adjustments in flow rate alone may not significantly impact the overall density unless they are coupled with changes in other factors. It reinforces the idea that under certain conditions, flow rate alone does not play a dominant role in influencing the product’s characteristics. In Figure 8c, the influence of temperature, in conjunction with sulfate concentration, on barium sulfate density is assessed. The data show that within the temperature range of 70 °C to 80 °C, fluctuations in temperature have a negligible effect on density. This suggests that when sulfate concentration is controlled, temperature changes do not substantially affect the precipitation process, pointing to the limited role of temperature within the studied range. Finally, Figure 8d examines the interaction between temperature and flow rate. The relatively flat surface in this plot indicates that neither temperature nor flow rate, within the ranges tested, significantly influences the density of barium sulfate. This suggests that there exists a threshold beyond which further changes in these parameters do not substantially alter the final density of the product. This observation implies that optimizing these variables might be less critical compared to other factors, such as concentration. The relatively insensitive nature of barium sulfate density to variations in temperature and flow rate, as indicated in Figure 8c,d, suggests that temperature and flow rate adjustments beyond certain thresholds do not significantly alter the physical characteristics of the product. This finding is consistent with the concept of thermodynamic equilibrium, where the synthesis conditions may reach a point beyond which further changes in temperature or flow rate yield diminishing returns in terms of product properties. Overall, the response surface methodology presented in Figure 8 emphasizes the importance of optimizing reactant concentrations to achieve the desired barium sulfate density. It also illustrates the relatively minor impact of temperature and flow rate variations within the experimental ranges. These insights are valuable for the development of efficient and cost-effective strategies for barium sulfate synthesis, offering a pathway for optimizing the process and improving product yield.

3.2. Optimization Conditions

The optimal conditions for this process were determined by the software as follows: under the experimental optimum conditions, BaCl₂ concentration = 1.5 M, SO₄²⁻ concentration = 0.41 M, flow rate = 2.53 mL/min, and temperature = 20.03 °C. Under these conditions, the software predicted the production of 9.21 g of barium sulfate with a density of 4.25 g/cm³. The optimal condition tests were repeated three times, yielding the results presented in

Table 6. Experimental results and average values for barium sulfate synthesis under optimized conditions.

Test No.	Mass (g)	Density (g/cm3)
1	9.11	4.29
2	9.27	4.2
3	9.23	4.26
Average	9.20	4.25

. This shows that the experimental values closely align with the predicted output, confirming the reliability of the model.

Table 7. The XRF analysis results of synthesized barium sulfate.

Component	%	Component	%
Potassium Oxide (K2O)	0.04	Cadmium Oxide (CdO)	0.025
Sodium Oxide (Na2O)	0.12	Silver Oxide (Ag2O)	0.023
Iron(III)7Oxide (Fe2O3)	0.011	Copper Oxide (CuO)	0.014
Strontium Oxide (SrO)	0.33	Chlorine (Cl)	0.93
Aluminum Oxide (Al2O3)	0.82	Calcium Oxide (CaO)	0.083
Barium Oxide (BaO)	62.44	Phosphorus Pentoxide (P2O5)	0.017
Sulfur Trioxide (SO3)	33.64	Magnesium Oxide (MgO)	0.027

displays the results from the X-ray fluorescence (XRF) analysis of barium sulfate synthesized under optimum conditions. The XRF analysis clearly supports the notion that the synthesis method employed produces barium sulfate of exceptional purity (high elemental purity), which is critical for industries that require high-quality materials, such as pharmaceuticals, ceramics, and cosmetics. The minute quantities of impurities (e.g., Al₂O₃ and SrO) are within acceptable thresholds for proposed applications, ensuring the integrity of the end product for stringent industrial uses. These minor quantities of impurities are due to the use of industrial-grade purity reagents. The most notable observation from the data is the absence of significant impurities such as silica and potassium oxide, which are often problematic in synthesizing materials. The presence of minor traces of aluminum oxide (Al₂O₃) and strontium oxide (SrO) further emphasizes the controlled nature of the synthesis process, where such components are kept to minimal levels. This result affirms the robustness of the synthesis method, which could be of great interest to industries requiring barium sulfate with high performance characteristics. The average purity of the barium sulfate was determined to be 96.08%.

The high purity of the synthesized barium sulfate, coupled with its low levels of contaminants, demonstrates the suitability of the product for critical industrial applications where impurity levels must be carefully controlled. The method presented here could serve as a valuable contribution to improving existing production systems for barium sulfate, especially for industries that demand high grades of material for their processes. Furthermore, the scalability of this synthesis method holds promise for industrial-scale production. Given the efficiency in achieving high purity and the low operational costs, this technique could offer a pathway for more sustainable and economically viable large-scale manufacturing of barium sulfate.

4. Conclusions

This study successfully developed a methodology for the synthesis of barium sulfate at the laboratory scale. Using the D-optimal design, critical reaction parameters—such as barium chloride and sulfate concentrations—were systematically optimized. Under the experimental optimum conditions—BaCl₂ concentration = 1.5 M, SO₄²⁻ concentration = 0.41 M, flow rate = 2.53 mL/min, and temperature = 20.03 °C—9.21 g barium sulfate with a density of 4.25 g/cm³ can be achieved. The experimental results and corresponding average values for barium sulfate synthesis under optimized conditions demonstrate that, on average, 9.20 g of barium sulfate with a density of 4.25 g/cm³ was produced. This shows that the experimental values closely align with the predicted output, confirming the reliability of the model. The analysis of barium sulfate produced in the optimum conditions confirmed the purity, with a barium oxide content of 62.44% and sulfur trioxide at 33.64%, verifying the material’s industrial applicability. The robustness and reliability of the optimization process were validated through rigorous statistical analysis, which demonstrated strong predictive capabilities with high F-values and R² indicators for both mass and density outcomes. Future research should focus on scaling the process for large-scale industrial applications and exploring additional variables that could further enhance production efficiency and sustainability.