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. 2026 Jun 1;11(23):33663–33671. doi: 10.1021/acsomega.5c13246

Recovery Yield and Defective Product Rate in a Bio-Based Amino Acid Crystallization Process

Jin Tae Hong †, Jin Joo Oh †, Jung Won Park †, Byeongchan Ahn ‡, Wangyun Won ‡,*, Jun-Woo Kim †,§,∥,*
PMCID: PMC13280909  PMID: 42326708

Abstract

The design and evaluation of biobased processes involving crystallization can be challenged owing to the lack of experimental data, leading to inaccurate predictions. This study presents a method for predicting the crystal purity and recovery yield of biobased amino acids, including l-alanine (ALA), l-histidine monohydrochloride monohydrate (HIS), and l-citrulline (CIT), in evaporative crystallization processes. An effective distribution model was proposed to describe the relationship between liquid and crystal purity by using an empirically modified logistic curve. By coupling mass balance with an effective distribution model, a method to predict the crystal purity was developed on the basis of the feed purity and recovery yield of the crystallization process. Furthermore, a statistical approach was applied to predict the defective product disturbances. Our results demonstrate that HIS achieves a higher crystal purity more easily than does ALA. Additionally, a quantitative analysis revealed that for all amino acids, the defective product rate decreases as the target crystal purity increases and minimum specification purity decreases. This study provides a basis for considering downstream recovery yield as an important metric in the design and evaluation of biobased processes involving crystallization.

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1. Introduction

Rapid advancements in biotechnology have significantly increased the requirements for comprehensive design and evaluation of biobased material production, such as technoeconomic analysis (TEA) and life cycle assessment (LCA). When the final product is in a crystalline form, the crystallization process becomes one of the most significant stages, as it directly influences both product quality and recovery yield. − However, during the evaluation of biobased crystalline products, experimentally validated data based on industrial process streams are often not considered. − Instead, the assumed crystallization recovery yield and crystal purity derived from analogous systems are frequently applied. These assumptions can considerably reduce the accuracy of the process design and evaluation outcomes.

Succinic acid can be produced from feedstocks such as glucose, cassava root, and spent sulfite liquor using Actinobacillus succinogenes. It has been experimentally demonstrated that succinic acid with a purity of 90–99% can be recovered through direct crystallization, at recovery yields of 57–93%. − In 2022, Tomczyk et al. conducted a TEA on the conversion of renewable sugars from corn stover feedstock to succinic acid using A. succinogenes. The crystal purity of the succinic acid obtained through direct crystallization by cooling to 4 °C was assumed to be 99.7%, although the assumed crystallization recovery yield was not explicitly stated. In 2023, Thanahiranya et al. performed both TEA and LCA to convert glycerol into succinic acid using A. succinogenes. The crystal purity obtained after direct crystallization was assumed to be 99.5%; however, the crystallization recovery yield was not clearly specified.

Unlu et al. conducted a TEA on the production of muconic acid from biorefinery lignin residue using Pseudomonas putida, followed by its conversion to adipic acid. The recovery yield of muconic acid was reported to be 81.4%, with a crystal purity of 99.8%, based on the experimental data by Vardon et al. However, the subsequent crystallization yield and purity of adipic acid were assumed to be 100% and 99.8%, respectively, without experimental evidence from biobased process liquids, relying solely on pure solubility data. Magalhães et al. conducted a TEA of the downstream process of an itaconic acid fermentation broth from glucose using Aspergillus terreus. Although they designed an industrial crystallization process based on crystallization residence time and target size, no substantial experimental evidence has been provided to predict the recovery yield and crystal purity.

Because biobased feed liquids for crystallization typically contain a wide variety of impurities, obtaining an accurate relationship between the crystal purity and recovery yield requires a crystallization process development stage that is both time-consuming and resource-intensive. However, the most reliable results can be ensured for biobased crystalline products with available plant data from commercial production, as in our previous study on the LCA of l-methionine and l-lysine. , However, this approach is not feasible for early-stage evaluations. The most practical alternative for early-stage design and evaluation is to conduct crystallization experiments under fixed conditions, similar to the actual production environments, to obtain limited data, including crystal purity and recovery yield.

In industrial crystallization processes, crystal purity is determined by the complex interactions of various process factors, such as agglomeration, surface washing efficiency, liquid inclusion, and solid solution formation. Recently, a method was proposed to express these comprehensive phenomenological results using the distribution coefficient, which is defined as the ratio of the actual impurity concentration in a crystal to that in a bulk liquid. , This can be seen as an attempt to apply the concept of the effective distribution coefficient (represents the ratio of the actual impurity concentration in the crystal to that in the bulk liquid), which is often used in melt crystallization, to industrial slurry crystallization. − Although the effective distribution coefficient does not have a strict thermodynamic meaning, it is similar to the general trend of distribution diagrams influenced by solid solutions, which are commonly encountered in amino acids. −

The main contributions of this study can be summarized as follows: (1) effective distribution data was experimentally obtained for biobased materials, such as l-alanine (ALA), l-histidine monohydrochloride monohydrate (HIS), and l-citrulline (CIT), which can be utilized in the development of industrial processes for newly developed biobased substances. (2) An empirical mathematical model was proposed to interpret the effective distribution data, thereby developing a method for quantitatively predicting the crystal purity and recovery yield. (3) A statistical approach was formulated to predict the defective product rate based on the distribution of crystal purity residuals under process disturbances while considering the target crystal and minimum specification purities. 4) It was suggested that, in addition to the titer, rate, and yield metrics in a fermentation process, − which are significant in the design and evaluation of biobased processes, the downstream recovery yield metric should also be considered important.

2. Materials and Methods

2.1. Materials

Processing liquids containing ALA, HIS, and CIT were provided by CJ CheilJedang Co. (South Korea). All these process liquids originated from a fermentation broth containing Corynebacterium glutamicum strains, and the cells were removed through membrane separation. Subsequently, the purities of the processed liquids were adjusted through fractional or mother liquid crystallization. The contents of the target material on a dry basis, referred to as “purity” in industrial terms, were adjusted to 27.9–96.8% for ALA, 18.5–95.4% for HIS, and 26.1–96.7% for CIT. The target material mainly consisted of amino acids, organic acids, sugars, and inorganic electrolytes. However, the detailed compositions were not disclosed owing to confidentiality. l-Alanine (≥99.5%; Sigma-Aldrich, MO, US), l-histidine monohydrochloride monohydrate (≥99.5%; Sigma-Aldrich, MO, US), and l-citrulline (≥98%; Sigma-Aldrich, MO, US) were used as standard reagents for high-performance liquid chromatography (HPLC) measurements. 1-Octanesulfonic acid sodium salt (OSA; ≥98%; Sigma-Aldrich, MO, US), potassium phosphate monobasic (≥99.0%; Sigma-Aldrich, MO, US), phosphoric acid (≥85% in H2O; Sigma-Aldrich, MO, US), and acetonitrile (≥99.9%; Sigma-Aldrich, MO, US) were used for the preparation of the HPLC mobile phase. Triple-distilled water was prepared using in-house facilities.

2.2. Evaporative Crystallization

Evaporative crystallization experiments were conducted using an in-house 2 L jacketed glass evaporative crystallizer. The crystallizer had a cylindrical shape with an internal diameter of 1270 mm, and it could charge up to 2 L of the process liquid. The jacket was located outside the crystallizer, surrounding the crystallizer to half its height. To prevent scaling on the inner walls of the crystallizer owing to localized evaporative crystallization, which can occur if the process liquid level drops below the height of the jacket, the total volume of the process liquid was set to always remain above the height of the jacket. The bottom of the crystallizer had a rounded conical shape with an angle of approximately 25° for the easy discharge of the slurry after the completion of the experiment. A two-way Teflon valve was installed at the bottom of the crystallizer to allow the slurry discharge.

Stirring was performed using a Teflon-coated paddle-type impeller (width: 30 mm, height: 15 mm, and thickness: 4 mm) driven by an overhead stirrer (PL-SS20DW, Poonglim Tech, Korea) through a magnetic drive. The lower end of the impeller was positioned 30 mm above the bottom of the evaporative crystallizer. The stirring speed was set to 500 rpm to ensure that the crystal particles were mixed well without causing bubble formation owing to vortex.

Distilled water was used as the heating medium for the crystallizer jacket. The temperature of the heating medium was controlled at 80 °C using a circulation thermostat (DYNEO DD-310F, Julabo, Germany). A glass vapor–liquid separator was positioned at the top of the evaporative crystallizer, and it was connected to a glass condensate container and glass condenser. The glass condenser was coil type, with a diameter and height of 80 and 550 mm, respectively. To ensure sufficient condensation of the evaporated vapor, the temperature of the cooling medium was controlled at 5 °C using a circulation thermostat (DYNEO DD-310 FF, Julabo, Germany). A diaphragm vacuum pump (NVP-1000; Eyela, Japan) was used to evacuate the gas inside the crystallizer. The internal pressure of the crystallizer was maintained at 100 mbar using a digital pressure regulator (NVC2200; Eyela, Japan).

After evaporative crystallization, the crystal slurry was separated from the mother liquid using a basket centrifuge (H–110F, Kokusan, Japan). During the mother liquid separation stage, the centrifuge was operated at 3000 rpm for 10 min. The crystals were washed with distilled water to remove any remaining mother liquid from the crystal surfaces. The amount of wash water was set to 50 wt % of the expected crystal mass. During the washing and subsequent dewatering stages, the centrifuge was operated at 3000 rpm for 10 min. The wet crystals were then evenly spread on a stainless-steel tray and placed in a convection oven (BF 360PO, Bio Free, Korea) controlled at 70 °C, where samples were dried for 24 h until no change of weight. In this study, the terms ‘initial’ and ‘final’ refer to the crystallization feed state and the dried crystal state, respectively.

2.3. Crystal and Process Liquid Characterization

The size and morphology of the dried crystals were observed using an optical microscope (BX53; Olympus, Japan). The dry weight fraction was measured using a moisture analyzer (HC 103, Mettler Toledo, Switzerland) following a loss on drying method. The drying temperature was set to 105 °C, and the process continued until weight became constant. The liquid was evenly distributed on a filter paper (Whatman, grade No. 2, UK) to ensure complete drying. The contents of the target material in both the crystals and experimental liquid were measured using HPLC. The measurement conditions are summarized in Table .

1. Summary of HPLC Measurement Conditions.

target material ALA HIS CIT
instrument HPLC 1260 Infinity system (Shimadzu, Japan) HPLC 1260 Infinity system (Shimadzu, Japan) HPLC 1260 Infinity system (Shimadzu, Japan)
column CAPCELLPAK C18 AQ 3 μm; 4.6 mm × 250 mm (Shiseido, Japan) ACQUITY C18 BEH 1.7 μm; 2.1 mm × 50 mm (Waters, MA, US) ACQUITY UPLC BEH C18 1.7 μm; 2.1 × 150 mm (Waters, MA, US)
mobile phase mobile phase A (14 mM OSA +25 mM KH2PO4 in water; pH: 2.1 controlled by H3PO4); mobile phase B (14 mM OSA +25 mM KH2PO4 in 50% acetonitrile aqueous solution; pH: 2.1 controlled by H3PO4); mobile phase A/mobile phase B = 95:5 mobile phase A (14 mM OSA +25 mM KH2PO4 in water; pH: 2.1 controlled by H3PO4); mobile phase B (14 mM OSA +25 mM KH2PO4 in 50% acetonitrile aqueous solution; pH: 2.1 controlled by H3PO4); mobile phase A/mobile phase B = 72:28 13.5 mM OSA +25 mM KH2PO4 in water; pH: 2.1 controlled by H3PO4
flow rate 1.00 mL/min 0.25 mL/min 0.30 mL/min
temperature 40 °C 40 °C 40 °C
detection ultraviolet (UV) at 210 nm UV at 210 nm UV at 210 nm
sample injection volume 3 μL 1 μL 2 μL
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2.4. Effective Distribution

A Roozeboom diagram is a type of distribution diagram that represents the solvent-free composition of a target material in both the liquid and solid phases in a two-dimensional graph. It can effectively illustrate the correlation between the solvent-free purity of the processed liquid and the purity of the crystals during crystallization. , Although the Roozeboom diagram typically represents the thermodynamic equilibrium between the liquid and solid phases, a similar form of an effective distribution diagram can be constructed by using an effective solvent-free composition, even if phase equilibrium has not been reached. This approach provides valuable information for industrial crystallization processes, because it considers various factors that can influence the crystallization process.

During crystallization, crystals do not typically achieve homogeneous compositions because of the significantly slower mass transfer rate in the solid phase. Therefore, in batch crystallization processes, the solvent-free composition of the liquid and crystals changes as the process progresses. The weight fraction of the target material on a solvent-free basis in the solid phase, commonly referred to as “crystal purity” in industrial terms (w X ), was determined by measuring the solvent-free composition of the crystals. The weight fraction of the target material on a solvent-free basis in the liquid phase, commonly referred to as “liquid purity” in industrial terms (w X ), was experimentally determined by averaging the liquid purity of the crystallization feed and mother liquid.

The effective distribution data obtained from the above experiments do not have thermodynamic significance. Therefore, it is not appropriate to represent the effective distribution using conventional phase equilibrium models. Instead, an appropriate empirical model that could effectively explain the physical phenomena was applied. In this study, the following modified logistic curve model was applied

wXsf,sol=L1+e−k(wXsf,liq−a)+b 1

where L, k, a, and b are parameters of the modified logistic curve model. If b is 0, the model is reduced to a general logistic curve model, where L, k, and a represent the supremum of the function values, steepness of the curve, and midpoint of the function values, respectively. The general logistic curve model can yield negative x-axis values or x-axis values greater than 1, which present a problem because these values are physically impossible when the x-axis is defined as the weight fraction. Therefore, to avoid physical inconsistencies, parameter b was applied with the following constraints

b=1+ek(1−a)1−ek 2
L=−b(1+eka) 3

On applying these constraints, the modified logistic curves in eq becomes a model with only two parameters, namely, a and k. Based on the constraints given by eqs and (), when w X is 0, w X is also 0. Similarly, when w X is 1, w X is also 1. When w X has a value between 0 and 1, w X will also have a value between 0 and 1. This reflects the physical characteristics of the effective distribution. The parameters k and a were determined from the experimental data via the root mean squared error (RMSE) method using the Microsoft Excel Solver plug-in. Figure shows the effective distribution diagrams of valine–alanine, valine-norvaline, valine–isoleucine, and valine–leucine systems with the calculation results using eqs –.

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Effective distribution diagrams of the literature data based on the results calculated using eqs –.

2.5. Crystal Purity and Recovery Yield

The crystal purity (w X ) after evaporative crystallization was calculated using the following integral equation

wXsf,sol=∫wX,fsf,liqwX,isf,liq(L1+e−k(wXsf,liq−a)+b)dwXsf,liqwX,isf,liq−wX,fsf,liq 4

where w X, i and w X, f are the initial and final weight fraction of the target material on a solvent-free basis in the liquid phase, respectively. In other words, w X, i and w X, f are defined as the crystallization feed purity and mother liquid purity, respectively. The integral terms in eq have an analytical solution that simplifies the calculation.

Crystal purity also can be expressed by the following mass balance equation

wXsf,sol=wX,isf,liqRXwX,isf,liqRX+(1−wX,isf,liq)RY 5

where R X and R Y represent the recovery yields of the target material and impurities in the crystal, respectively. Given w X, i and R X, R Y can be numerically calculated using an objective function that minimizes the difference in w X obtained from eqs and (). In this study, R Y was calculated via the RMSE method using the Microsoft Excel Solver plug-in. The crystal purity and recovery yield are the most significant aspects in the design and evaluation of industrial production. Notably, such simulations are possible even in the absence of solubility data.

2.6. Defective Product Rate

In an actual crystallization process, even with the same crystallization feed purity and target recovery yield, the crystal purity of the final product may vary because of various disturbances. During the development process, the impact of these disturbances is represented by the residual crystal purity, which is the difference between w X, calc calculated using eq and w X, exp obtained from actual experiments. The subscripts calc and exp refer to the calculated and experimental values, respectively. In this study, outliers in the crystal purity residuals were removed using the interquartile range method, and the normality was tested using the Shapiro–Wilk test. Subsequently, a statistical analysis was conducted to simulate the crystal purity distribution upon obtaining the crystallization feed purity and target crystal purity. Finally, the defective product rate was predicted on the basis of the minimum specified purity and target crystal purity. In this study, the defective product rate is the probability of the fraction of final crystal products that do not satisfy the predefined quality specification. Specifically, a defective product refers to a final crystal product whose crystal purity is lower than the minimum specification purity. Because long-term plant-scale production data were not available, the defective product rate was statistically estimated from the distribution of the crystal purity residuals. The residual crystal purity was assumed to follow a normal distribution, with the mean and standard deviation obtained from the experimental residuals for each amino acid. Therefore, for a given target crystal purity, the defective product rate was calculated as the lower tail probability that the actual crystal purity falls below the minimum specification purity.

3. Results and Discussion

3.1. Crystal Morphology and Size

Optical microscopy images of the ALA, HIS, and CIT crystals are shown in Figure . The morphology of the ALA crystals in Figure a resembles the rod-like morphology of ALA crystals in pure water reported in the literature. ALA crystals can sometimes exhibit a needle-like morphology depending on the additives used, leading to an increase in the aspect ratio of the lower-purity ALA crystals (Figure b) compared to the higher-purity ALA crystals (Figure a). The morphology of the HIS crystals in Figure c is column-like, which is similar to that of the HIS crystals in pure water reported in the literature. Similar to ALA, the lower-purity HIS crystals in Figure d show a relative increase in aspect ratio compared to the higher-purity HIS crystals in Figure c. The morphology of the CIT crystals shown in Figure e is similar to the column-like morphology of commercial CIT reported in the literature. Similar to the other samples, the lower-purity CIT crystals in Figure f show a relative increase in aspect ratio compared to the higher-purity CIT crystals in Figure e. The increase in the aspect ratio is a dynamic factor that can decrease the crystal purity by reducing washing efficiency. In addition, in all cases, the particle size tended to decrease with decreasing crystal purity. Furthermore, the decrease in the crystal size is a dynamic factor that can decrease the crystal purity by reducing washing efficiency.

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Optical microscopic images of the crystal samples: ALA of purity at 99.8% (a), ALA of purity at 75.5% (b), HIS of purity at 99.8% (c), HIS of purity at 70.3% (d), CIT of purity at 99.8% (e), and CIT of purity at 73.8% (f).

3.2. Effective Distribution Model

Figure shows the effective distribution diagrams of ALA, HIS, and CIT. Table presents the regression results for the effective distribution models of ALA, HIS, and CIT obtained using eqs –, along with the coefficient of determination (R 2 ). As shown in Figure , the effective distribution of HIS was positioned farthest to the upper-left compared to the other materials. This indicates that HIS is the easiest to purify because it is more likely to produce high-purity crystals. In contrast, the effective distribution of ALA was positioned farthest to the lower-right, suggesting that obtaining high-purity ALA crystals is more difficult. The effective distribution of CIT was found to have a tendency between that of HIS and ALA.

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Effective distribution diagram of ALA, HIS, and CIT, based on the results calculated using eqs –.

2. Parameters and R 2 for eqs – for the Effective Distribution of ALA, HIS, and CIT.

target material k a R 2
ALA 7.226 0.07128 0.8550
HIS 10.69 –1.183 0.3629
CIT 7.123 –1.182 0.4200
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The effective distribution diagrams for ALA, HIS, and CIT showed a steep increase at low liquid purities that gradually leveled off toward a plateau. This indicates that the distribution coefficients of ALA, HIS, and CIT exceed one across all intervals, implying that obtaining the desired high-purity crystals through fractional crystallization is possible even though the actual manufacturing conditions and economic considerations were not considered. However, one limitation of this study is that no data were obtained for any of the materials in the region where w X was below 70%. If the experiments are extended to this region, then there is a possibility that the effective distribution may take on an S-shaped curve. In such cases, the distribution coefficient will fall below 1 in the lower w X range. However, no point where the solid- and liquid-phase compositions become identical was observed in the present data. , Generally, amino acid crystallization is performed to obtain high-purity products, and the low-purity region was not the focus of this study; therefore, it is not a critical issue. However, if there is a requirement to extend to a low-concentration region, such as when recovering electrolyte byproducts from a purged mother liquid, , experimental data in the low-purity region would be necessary.

The effective distribution diagram presented here does not have any thermodynamic significance and is directly influenced by process dynamics. This means that if there are significant changes in the relative processes, such as fermentation, feed pretreatment, crystallization, separation, and washing, then the accuracy of the existing effective distribution diagram may decrease. Therefore, to maintain high reliability, the diagram must be updated by using new experimental data. This implies that when designing or evaluating bioprocesses under different fermentation and downstream process conditions, relying on crystallization research data from other conditions without conducting crystallization appropriate studies for the new conditions can lead to reduced reliability. In other words, if the process conditions change, then using crystallization yield data from previous experiments (under different conditions) without revalidation through crystallization experiments could result in significant undesired errors.

3.3. Crystal Purity Simulation

Figure presents the simulation results of the effects of the recovery yield and feed purity on the crystal purity obtained using eqs and (). In all cases, as the recovery yield increased, crystal purity decreased. Furthermore, crystal purity increased as the feed purity increased. Although these results were expected, a quantitatively accurate prediction is of significant practical value for industrial applications. As shown in Figure , for the same feed purity and recovery yield, HIS has the highest crystal purity compared to the other two materials. Conversely, ALA exhibits the lowest crystal purity under identical feed purity and recovery yield conditions. CIT showed a trend between those of HIS and ALA. This aligns with the trends described for effective distribution, as shown in Figure .

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Simulation results showing the effect of recovery yield and feed purity on the crystal purity of ALA (a), HIS (b), and CIT (c).

The decrease in crystal purity with an increasing recovery yield is characterized by a gradual slope at low recovery yields, which becomes steeper at high recovery yields. This is due to the concave downward increasing shape of the effective distribution for all the materials (Figure ). Most industrial processes aim to achieve crystallization with high recovery yields to maximize the economic benefits. However, at high recovery yields, even a slight increase in the yield can lead to a rapid decrease in the crystal purity, as shown in Figure . This suggests that precise and stable operations are essential for industrial crystallization processes.

The sensitivity of the crystal purity to feed purity can be determined by observing the changes in crystal purity within the same feed purity interval. As shown in Figure , for ALA, crystal purity is highly sensitive to the feed purity. However, the crystal purity of HIS showed the lowest sensitivity to the feed purity. This implies that improving feed purity, such as by using high-purity raw materials, improving the fermentation process, activated carbon treatment, resin adsorption, and chromatography, could be significantly effective in enhancing the crystal purity of ALA.

If the recovery yield reaches 100% and there are no processes that cause purity changes, such as thermal decomposition and biological degradation, the crystal purity converges to the feed purity. Although such a scenario is difficult to achieve during crystallization, it is possible in a granulation process combined with a drying process. During the granulation and drying processes, most of the solvent is removed from the feed, and the remaining substances form solid particles. Although this study does not focus deeply into this subject, the granulation process has been commercially implemented for bioderived amino acids such as l-lysine, l-threonine, l-tryptophan, l-valine, and l-isoleucine. − Additionally, relatively low-purity granulated amino acids, such as l-lysine, l-threonine, l-tryptophan, and l-valine, have been registered with the U.S. Food and Drug Administration (FDA) under the current animal food generally recognized as safe (GRAS) notification after thorough safety evaluations.

The simulation results in Figure provide information only on the impact of the increase in the recovery yield on the crystal purity. However, in actual industrial evaporative crystallization processes, it is not feasible to increase the concentration infinitely to improve the recovery yield. Increasing the concentration of the crystallization slurry leads to an increase in viscosity, which can reduce the evaporation rate owing to excessively high viscosity or failure to maintain the minimum required fluidity for operating an industrial evaporator. Therefore, a possible alternative for practical industrial applications is to divide the crystallization process into multiple stages of mother liquid crystallization. For example, evaporative crystallization can be carried out until an appropriate target viscosity is reached, followed by crystal-mother liquid separation. The mother liquid generated from the separation process will undergo the next stage of evaporative crystallization. By repeating these stages, the recovery yield can be increased without causing excessive viscosity problems. Another alternative is to recycle a portion of the mother liquid into the crystallization feed. − This mother liquid recycling method is economical when the fixed cost of an evaporator is high.

3.4. Crystal Purity Residual Distribution

Figure shows the crystal purity residuals of ALA, HIS, and CIT, along with the cumulative normal distribution. Table summarizes the Shapiro–Wilk test results for the crystal purity residuals of ALA, HIS, and CIT. The ALA crystal purity residual data ranged from −0.02375 to 0.03154 with a mean and standard deviation of 0.003366 and 0.01031, respectively. The HIS crystal purity residual data ranged from −0.02953 to 0.02747 with a mean and standard deviation of −0.001939 and 0.01201, respectively. The CIT crystal purity residual data ranged from −0.02439 to 0.03076 with a mean and standard deviation of 0.001238 and 0.01102, respectively. According to a Shapiro–Wilk test, the crystal purity residuals of all materials follow a normal distribution, with p-values exceeding 0.05. This indicates that normality was statistically significant in all cases. Figure confirms that the cumulative normal distribution closely matches the crystal purity residuals of ALA, HIS, and CIT. This provides a basis for using the crystal purity residuals to statistically interpret the defective product rate through the application of a normal distribution.

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Crystal purity residuals of ALA, HIS, and CIT with cumulative normal distributions.

3. Shapiro–Wilk Test Results for the Crystal Purity Residuals of ALA, HIS, and CIT.

target material Shapiro–Wilk statistics p-value
ALA 0.09152 0.8701
HIS 0.1438 0.06332
CIT 0.1200 0.2525
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3.5. Defective Product Rate Simulation

Figure shows the defective product rates of ALA, HIS, and CIT as functions of the target crystal purity and the minimum specification purity. Here, the defective product rate does not indicate an independently measured plantwide defect rate. Rather, it represents a model-based estimate of the probability that the final crystal purity becomes lower than the minimum specification purity under process disturbances. The target crystal purity refers to the desired crystal purity in the crystallization process, which can be controlled by adjusting the recovery yield, as shown in Figure . As shown in Figure , the defective product rate decreased as the target crystal purity increased in all cases. In addition, the defective product rate increased as the minimum specification purity increased in all cases. Although these results were expected, these quantitative simulations are beneficial to the design and operation of commercial processes.

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Defective product rate of ALA (a), HIS (b), and CIT (c) according to the target crystal purity and the minimum specification purity.

When the minimum specification purity is relatively low, setting a sufficiently high target crystal purity can reduce the defective product rate to ∼0%. For example, when the minimum specification purity is 90% and the target crystal purity is 94%, the defective product rate is approximately 0% in all cases. Similarly, when the minimum specified purity is 95% and the target crystal purity is 99%, the defective product rate is approximately 0% in all cases. Interestingly, targeting a crystal purity of 98% at a purity of 100% still resulted in defective products. This phenomenon became more pronounced as the standard deviation of the residual crystal purity increased, indicating stronger process disturbances. This suggests that when aiming for a minimum specification of high purity, merely increasing the target crystal purity may not be sufficient to achieve goals such as the 6-sigma initiative, which aims to maintain a defective product rate below a six-sigma level (0.00034%) in manufacturing processes. Instead, it may be necessary to reduce the deviations caused by process disturbances.

Increasing the target crystal purity to reduce the defective product rate has the drawback of decreasing the recovery yield. However, if the recovery yield is increased to reduce costs, then the target crystal purity decreases, and the defective product rate will increase. Furthermore, these defective products will need to be reprocessed for the conversion into high-purity products. The most common method for reprocessing defective products into high-purity products is recrystallization, which is a type of fractional crystallization. Economic optimization can be achieved by minimizing the total cost, which includes the cost increase from reprocessing defective products into high-purity products and loss cost increase due to the decrease in recovery yield. This optimization can be accomplished by setting the total cost as an objective function.

For example, if the feed purity, minimum specification purity, and target crystal purity for ALA are assumed to be 90, 98, and 99%, respectively, the recovery yield and defective product rate would be 82.0 and 9.73%, respectively, as shown in Figures a and a. The prices of ALA in the crystallization feed and defective products are assumed as 5000 and 4000 USD/ton, respectively. In this case, the cost increase due to product loss is 1098 USD/ton, and the cost increase due to reprocessing defective products is 319 USD/ton, bringing the total objective cost function to 1417 USD/ton. If the target crystal purity is lowered to 98.5%, the recovery yield and defective product rate will be 87.5 and 20.9%, respectively, as shown in Figures a and a. In this case, the cost increase due to product loss will be 714 USD/ton and the cost increase due to the reprocessing of defective products will be 732 USD/ton, bringing the total objective cost function to 1446 USD/ton. This demonstrates that when the target crystal purity is lowered from 99% to 98.5%, although the recovery yield increases by 5.5%, an increase in the reprocessing costs for defective products results in an objective cost function increase of 29 USD/ton.

Generally, in the case of existing pharmaceutical, food, and feed-grade products, specifications have already been established. According to the food chemical codex, the assay specifications for ALA and HIS are set at 98.5–101.5%. In the United States Pharmacopeia, the assay specifications for ALA and CIT are 98.5–101.5 and 98.0–102.0%, respectively. When the specifications are already defined for a particular market, specification purity becomes a fixed variable that industrial producers cannot change arbitrarily. However, there are specific cases in which bioderived products can be commercialized after thorough safety verification. As of September 2024, l-methionine products with 85% and 90% purity have been commercialized under the current animal food GRAS notification managed by the FDA. Producing relatively low-purity products is expected to reduce manufacturing costs, and this can lead to a reduction in greenhouse gas emissions from an environmental perspective.

4. Conclusions

In this study, the relationship between liquid and crystal purities during the evaporative crystallization of ALA, HIS, and CIT was experimentally demonstrated and regressed using an effective distribution model with a modified logistic curve. In addition, by coupling the mass balance with the effective distribution model, the crystal purity was quantitatively predicted based on the crystallization feed purity and recovery yield. Finally, the defective production rate was statistically interpreted in relation to the target crystal and minimum specification purities from the distribution of crystal purity residuals. The results revealed that HIS was relatively easier to obtain as a high-purity crystal than the other two materials, whereas ALA was the most difficult to purify. Furthermore, in all cases, a decrease in the target crystal purity and an increase in the minimum specification purity led to an increase in the defective product rate. This study emphasizes the importance of the downstream recovery yield in the design and evaluation of biobased processes.

Acknowledgments

This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Climate, Energy & Environment (MCEE) of the Republic of Korea (RS-2024-00400653). The authors would like to acknowledge the financial support from Korea Environment Industry & Technology Institute (KEITI) through National R&D Program on Integrated Management Technologies for Global Carbon Regulations, funded by Ministry of Climate, Energy & Environment (MCEE) (RS-2025-02213127), and was carried out by the GHG Reduction Potential Assessment Consortium based on the Technology Database for Carbon Neutrality.

Jun-Woo Kim and Wangyun Won contributed to the topic’s conceptualization and supervision. Jin Tae Hong, Jin Joo Oh, Jung Won Park, and Byeongchan Ahn performed the data collection, computational simulations, and interpretation of the results. Jun-Woo Kim, Wangyun Won, Jin Tae Hong, Jin Joo Oh, Jung Won Park, and Byeongchan Ahn contributed to the manuscript’s writing and review.

The authors declare no competing financial interest.

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