Lactic Acid Production Process Research Articles

Efficient biorefinery process for lactic acid production from date wastes with alleviating substrate inhibition effect using thermo-alkaline repeated batch fermentation

In the current work, date wastes were used for lactic acid (LA) production under thermo-alkaline conditions to overcome some fermentation challenges. Amongst 27 bacterial isolates that produced LA from date juice, isolate D-218 exhibited better growth stability and LA production under various stressed conditions. This isolate was characterized as Bacillus coagulans D-218 using physiological and molecular identification methods. In batch fermentation mode, strain D-218 could not completely utilize 80 g/L of the total sugar and produced only 45.8 ± 2.8 g/L of LA at LA productivity of 0.214 g/L.h and high residual sugar (29.2 g/L) was unutilized in the fermentation media. Different repeated batch fermentations with different initial sugar concentrations and gradual increase in sugar concentrtions were conducted to maximize LA productivity. Starting with 60 g/L of total sugar, four runs of repeated batch fermentations were conducted that enhanced the LA productivity (70%) to 0.49 g/L.h. Another 9 runs were initiated with 40 g/L which further improved LA productivity that reached up to 0.77 g/L.h. Surprisingly, initiating fermentations with 20 g/L of total sugar successfully attained long-term fermentation (18 runs) with high LA yield and productivity without carbon loss of initiated startup sugar of date waste. In this process, strain D-218 could completely consume 80 g/L sugars with high LA production titer (72.9 ± 0.56 g/L), yield (0.92 g/g), and productivity (0.71 g/L.h). This study is the first to exploit date waste in a cost-effective system for high-titer lactic acid production under thermo-alkaline conditions (pH 9.0; 50 °C) and to report repeated batch fermentation for LA production from date wastes.

High-Titer Lactic Acid Production by Pediococcus acidilactici PA204 from Corn Stover through Fed-Batch Simultaneous Saccharification and Fermentation.

Lignocellulose comprised of cellulose and hemicellulose is one of the most abundant renewable feedstocks. Lactic acid bacteria have the ability to ferment sugar derived from lignocellulose. In this study, Pediococcus acidilactici PA204 is a lactic acid bacterium with a high tolerance of temperature and high-efficiency utilization of xylose. We developed a fed-batch simultaneous saccharification and fermentation (SSF) process at 37 °C (pH 6.0) using the 30 FPU (filter paper units)/g cellulase and 20 g/L corn steep powder in a 5 L bioreactor to produce lactic acid (LA). The titer, yield, and productivity of LA produced from 12% (w/w) NaOH-pretreated and washed stover were 92.01 g/L, 0.77 g/g stover, and 1.28 g/L/h, respectively, and those from 15% NaOH-pretreated and washed stover were 104.11 g/L, 0.69 g/g stover, and 1.24 g/L/h, respectively. This study develops a feasible fed-batch SSF process for LA production from corn stover and provides a promising candidate strain for high-titer and -yield lignocellulose-derived LA production.

Efficient two-step lactic acid production from cassava biomass using thermostable enzyme cocktail and lactic acid bacteria: insights from hydrolysis optimization and proteomics analysis.

Lactic acid is an intermediate-volume specialty chemical, used in the production of biodegradable polymers and other chemicals. Although lactic acid production process is well established, however, the cost of production is very high. Therefore, in this study; starchy biomass (cassava) was hydrolyzed with in-house enzyme cocktail prepared from Aspergillus foetidus MTCC508 and Bacillus subtilis RA10. Process optimization using Taguchi experimental design helped to optimize the most effective ratio of fungal and bacterial amylase for effective saccharification of cassava. A higher sugar yield of 379.63mg/gds was obtained under optimized conditions, using 30U/gds of bacterial enzyme and 90U/gds of the fungal enzyme at pH 4 within 48h of saccharification. Among 11 lactic acid bacteria isolated, Lactobacillus fermentum S1A and Lactobacillus farraginis SS3A produced the highest amount of lactic acid 0.81g/g and 0.77g/g, respectively, from the cassava hydrolysate. The study proved the potential renewable source of cassava biomass as a source for fermentable sugars that can be fermented to lactic acid with high yield. In future, this cost-effective and environmental-friendly bioprocess can be upscaled for industrial lactic acid production.

One-pot process for lactic acid production from wheat straw by an adapted Bacillus coagulans and identification of genes related to hydrolysate-tolerance

In this study, Bacillus coagulans CC17A with highly tolerant to hydrolysate was obtained through adaptive evolution. After 63 generations, the strain CC17A was stably in 45% (v/v) hydrolysate media and could digest multiple inhibitors in the hydrolysate. Based on its promising features, a one-pot process was developed to produce lactic acid (LA) from wheat straw. After dilute acid pretreatment of wheat straw, simultaneous saccharification and co-fermentation was conducted using CC17A without any solid-liquid separation and pre-detoxification. Total 35.50 g LA was produced from 80 g raw substrate and the production yield was as high as 70.9% of theoretical. To elucidate the tolerance mechanism, transcriptomic profiling of CC17A was studied. The highly up-regulated oxidoreductases and phenolic acid decarboxylase are considered to be involved with the inhibitors-tolerance of B. coagulans CC17A.

Steady States of a Fermentation Process for Lactic Acid Production at a Given Concentration of the Main Substrate

A computational scheme has been presented that generalizes theoretical representations of a technology for the continuous fermentation of lactic acid at a given concentration of the main substrate in the stream that enters a fermenter. The sequence of constructing the computational scheme includes a preliminary analysis and a principal analysis. In the preliminary analysis, relationships have been derived that form the region of estimating the boundary characteristics that correspond to a given productivity of the process. The coordinates of the point of the maximum productivity $$\left[ {{{S}_{{{\text{opt}}}}},{\kern 1pt} {\kern 1pt} {\kern 1pt} {{D}^{{{\text{opt}}}}}} \right]$$ have been found. The coordinates of singular points have also been determined: $$\left[ {{{S}_{1}}\left( {{{D}_{1}}} \right),{{D}_{1}}} \right]$$ for singular point 1, $$\left[ {{{S}_{2}}\left( {{{D}_{2}}} \right),{{D}_{2}}} \right]$$ for singular point 2, $$\left[ {{{S}_{3}}\left( {{{D}_{3}}} \right),{{D}_{3}}} \right]$$ for singular point 3, and $$\left[ {{{S}_{4}}\left( {{{D}_{4}}} \right),{{D}_{4}}} \right]$$ for singular point 4. For the point of the maximum productivity and singular points, relationships have been presented for calculating the initial concentrations of the main substrate S0 and the corresponding initial concentrations of the component that produces the substrate during fermentation M0. The values of coordinates have been constraints in constructing relationships for the principal analysis that determine sets for selecting the values of M0 and D at a given value of S0. The scheme of the construction of sets consists of three sections, namely, I, II, and III. The boundaries of these sections are determined by relationships (21), (22), and (23), respectively. The sequence of the construction of sets for each of the sections has been presented, and it has been shown that there is one set (Set1) for section I, there are two sets (Set1* and Set2*) for section II, and there are three sets (Set1**, Set2**, and Set3**) for section III. Tables have been given for calculating the elements of sets at a given value of S0. The theoretical relationships that have been derived are used for numerical calculation to estimate the characteristics of the multiplicity of steady states for each of the sets. It is shown that the range of the assignment of S0 is the widest for section I, whereas the range of values for the dilution rate D is the greatest for section III. Numerical estimates in a comparative variant for sets in sections II and III have shown that the final concentrations of components under the same initial conditions differ in the values of M0, M, and S. This makes it possible to obtain comparative estimates for the further processing of produced components (the recovery of lactic acid, the recycling and use of unconverted components, the recovery of a by-product, and so on).

Production of Lactic Acid from Banana Waste Peel by batch Fermentation using Lactic Acid Bacteria (LAB) isolated from Milk Products

Lactic acid is a chemical compound that plays a role in various biochemical processes and also widely used in the food, cosmetic, pharmaceutical, and chemical industries. The aim of this study was to establish a process of lactic acid (LA) production from organic banana peel waste using lactic acid bacteria isolated and growth in MRS media at 37ºC for 24 h from milk product. The results indicate that lactic acid production using lactic acid bacteria are identified as Gram-positive, non-spore forming rods, catalase-negative, usually nonmotile. There was significant pH difference from 5.64 to 3.92 in the fermentation production medium containing banana waste peel + inoculum and 5.64 to 3.89 in the medium containing banana waste peel extract + inoculum + malt extract during the course of time from 0 hours to 96 hours when compared to control containing only banana waste peel without inoculum. There was dramatic increase in the percentage of crude lactic acid production was similar along with change in pH from ranging from 6.14 to 6.71 before decolorization without activated charcoal and 7.31 to 7.53 after decolorization with activated charcoal for fermentation production medium during the course of 24 to 96 hours. Similarly, the percentage of crude lactic acid production increases ranging from 6.73 to 6.98 before decolorization without activated charcoal and 7.79 to 7.96 after decolorization with activated charcoal for fermentation production medium containing banana waste peel + Malt extract and inoculum from 0 to 96 hours. This may due to the high rate of consumption of starch compounds to lactic acid with the help of lactic acid bacteria.

Production of Raw Starch-Digesting Amylolytic Preparation in Yarrowia lipolytica and Its Application in Biotechnological Synthesis of Lactic Acid and Ethanol.

Sustainable economy drives increasing demand for raw biomass-decomposing enzymes. Microbial expression platforms exploited as cellular factories of such biocatalysts meet requirements of large-volume production. Previously, we developed Yarrowia lipolytica recombinant strains able to grow on raw starch of different plant origin. In the present study, we used the most efficient amylolytic strain as a microbial cell factory of raw-starch-digesting (RSD) amylolytic preparation composed of two enzymes. The RSD-preparation was produced in fed-batch bioreactor cultures. Concentrated and partly purified preparation was then tested in simultaneous saccharification and fermentation (SSF) processes with thermotolerant Kluyveromyces marxianus for ethanol production and Lactobacillus plantarum for production of lactic acid. These processes were conducted as a proof-of-concept that application of the novel RSD-preparation supports sufficient starch hydrolysis enabling microbial growth and production of targeted molecules, as the selected strains were confirmed to lack amylolytic activity. Doses of the preparation and thermal conditions were individually adjusted for the two processes. Additionally, ethanol production was tested under different aeration strategies; and lactic acid production process was tested in thermally pre-treated substrate, as well. Conducted studies demonstrated that the novel RSD-preparation provides satisfactory starch hydrolyzing activity for ethanol and lactic acid production from starch by non-amylolytic microorganisms.

Steady States of a Continuous Fermentation Process for Lactic Acid Production: The Multiplicity for a Given Dilution Rate

The results of an analysis of a generalized mathematical model for a continuous fermentation process for lactic acid production have been presented. The mathematical model includes a system of equations for the material balance of the main substrate (S), the substrate produced from raw materials during fermentation (M), biomass (X), a product (P), and a by-product (B). The kinetics of the formation of biomass (the equation for the specific rate μ) takes into account inhibition by the substrate, biomass, and product. An analysis has been performed from the standpoint of the possibility of estimating technological characteristics at a given dilution rate D (D = v/V, where v is the volumetric flow rate through a fermenter, m3/h, and V is the volume of the fermenter, m3). The limiting values of $$S{\kern 1pt} '$$ and D that ensure the practical implementation of the process have been estimated ( $$S{\kern 1pt} '$$ includes the initial concentrations of the main substrate S0 and the component that produces the substrate during synthesis M0). These characteristics have been designated as coordinates of “singular points.” The coordinates of a point that corresponds to the maximum productivity with respect to lactic acid QP ( $${{Q}_{P}} = DP,$$ where P is the concentration of lactic acid) have been determined simultaneously. Relationships have been derived for calculating sets of technological characteristics (the initial characteristics D, S0, and M0 and the current characteristics X, S, P, B, and M) based on a given value of D within permissible limits. It has been shown that, for the values of D that correspond to singular points (the first, second, and optimal points), there is one set and, for the other values of D, there are two sets. Numerical estimates of technological characteristics for the values of constants that correspond to the basic variant have been given. It has been shown that, with an increase in the productivity QP while approaching the value of max QP, the region of estimates of technological characteristics narrows. It has been recommended that the results of this study be used to predict the economic estimates of the implementation of particular conditions of a technological process.

Multi-Product Lactic Acid Bacteria Fermentations: A Review

Industrial biotechnology is a continuously expanding field focused on the application of microorganisms to produce chemicals using renewable sources as substrates. Currently, an increasing interest in new versatile processes, able to utilize a variety of substrates to obtain diverse products, can be observed. A robust microbial strain is critical in the creation of such processes. Lactic acid bacteria (LAB) are used to produce a wide variety of chemicals with high commercial interest. Lactic acid (LA) is the most predominant industrial product obtained from LAB fermentations, and its production is forecasted to rise as the result of the increasing demand of polylactic acid. Hence, the creation of new ways to revalorize LA production processes is of high interest and could further enhance its economic value. Therefore, this review explores some co-products of LA fermentations, derived from LAB, with special focus on bacteriocins, lipoteichoic acid, and probiotics. Finally, a multi-product process involving LA and the other compounds of interest is proposed.

A study of the residual fermentation sugars influence on an alternative downstream process for first and second-generation lactic acid

Lactic acid is an important biomolecule with a substantial market share. Currently, investments in the area are concentrated on new substrates and technologies, in order to boost production and separation performance. Molecular distillation has been recognized as a promising technology in the separation, purification, and concentration of natural products and hence with potential for application in the lactic acid production process. In this study, lactic acid was produced by fermentation using first (1G) and second-generation (2G) substrates, producing a complex mixture of lactic acid and residual sugars. The influence of the residual sugars, such as glucose, sucrose, and xylose, was investigated. For the 1G process, the results showed that the highest lactic acid concentration (99.51 g/L) can be obtained using the feed stream with the lowest sugars composition. For the 2G process, the highest lactic acid concentration reached (75.87 g/L) was lower than that observed for 1G experiments. The concentration of lactic acid using 1G or 2G lactic acid were, respectively, 2.73 times and 2.12 times higher than the initial raw material concentration, without the use of any extra solvent. The final process analysis showed that the use of molecular distillation for lactic acid downstream has different challenges to defeat for the separation of 1G and 2G lactic acid, which is relevant since many different feedstocks may be used in the lactic acid production.

Mathematical Modeling of the Fermentation Process for Lactic Acid Production: A Generalized Model

The results of the development of a generalized mathematical model for the fermentation method of lactic acid production have been presented. The mathematical model includes nonsteady-state equations for the production of biomass, the consumption of the substrate, and the production of lactic acid and metabolism byproducts and equations for the formation of an additional amount of the main substrate from the components of raw materials. We acquired the results of the modeling process using constants of the basic variant from studies. The dependences of the characteristics of the process on time for the basic variant and the dependence of the productivity of lactic acid (QP, g/(L h)) on time with estimation of time t reaching the maximum value of QP (max QP) have been presented. The mathematical model takes into account all possible variants of inhibition, namely, concerning the biomass, product, and substrate. The results of modeling with allowance for the intensity of inhibition from each of the factors have shown the following. An increase in biomass inhibition constant Xmax decreases the duration of the process, an increase in product inhibition constant Pmax slightly increases the duration of the process, and a decrease in substrate inhibition constant Ki (the intensity of inhibition increases) considerably increases the duration of the process. Time of process completion tk for all conditions of modeling was determined by reaching one of the following conditions: X = Xmax or P = Pmax or S = 0. In modeling, it has also been found that the variation of constants in the equation for the formation of byproducts does not affect the variation in the characteristics of the process except for the numerical value of the concentration of byproducts.

Model-based temperature control for improving lactic acid production from glycerol.

To maximize the final lactic acid productivity and concentration, temperature control was optimized using a mathematical modelling approach. A kinetic model, including cell growth, product formation and substrate consumption equations, was proposed to describe the lactic acid production process by Escherichia coli AC-521 with glycerol as the substrate. By constructing four functions, the temperature effect was introduced on the fermentation process, where four parameters (Xmax, μmax, Yps and β) were observed to be significantly affected by the temperature. For the convenience of application, the temperature control strategies were simplified by dividing the whole fermentation process into several units. In each unit, the temperature was controlled constantly. Based on the model, the optimal temperature for each unit was determined to maximize the final lactate productivity. This temperature control strategy can be effectively applied in batch and fed-batch cultures, and the verified experimental evaluation showed a good correlation with the model data. Under improved temperature control conditions, a maximal lactic acid concentration of 90.4 g L−1 was obtained after 80 h of fed-batch fermentation, giving a productivity of 1.13 g L−1 h−1, which is 1.2 times more than that in the conventional constant temperature during the cultivation course.

One step open fermentation for lactic acid production from inedible starchy biomass by thermophilic Bacillus coagulans IPE22

The aim of this study was to establish a simplified operational process for lactic acid (LA) production by Bacillus coagulans IPE22 from inedible starchy biomass with open fermentation method. First, 29.47 mU/mg specific amylase activity was detected in direct batch fermentation from soluble starch, but the activity of the produced amylase was too low for effective production of LA. Then seven batches from 72 g/L soluble starch were conducted without sterilization. It was found that one step simultaneous liquefaction, saccharification and fermentation (SLSF) with the addition of mesothermal α-amylase and glucoamylase was the optimal mode with LA concentration, yield and productivity of 68.72 g/L, 0.99 g/g and 1.72 g/L h respectively. Finally, inedible starchy biomass, cassava and sorghum flours, were proved to be alternatives to refined soluble starch. For the first time, one step open SLSF of inedible starchy biomass was reported for LA production by B. coagulans.

Exploring cellular fatty acid composition and intracellular metabolites of osmotic-tolerant mutant Lactobacillus paracasei NCBIO-M2 for highly efficient lactic acid production with high initial glucose concentration

High titer, productivity and yield are the main pre-requisites of an efficient lactic acid production process. However, the hyperosmotic stress inhibits cell metabolism in the later phase of fermentation. In this study, an osmotic-tolerant mutant named Lactobacillus paracasei NCBIO01-M2 was obtained through a high-throughput screening technology, which exhibited a higher tolerance to osmotic stress due to its more flexible regulation of the unsaturated fatty acid proportion along with the intracellular compatible solute pools. The mutant successfully consumed all 248 g/L initial glucose and produced 223.7 g/L lactic acid with a productivity of 5.53 g/L/h in a single batch fermentation by the neutralizing agent strategy. Moreover, similar fermentation performances were also achieved in the open fermentation mode without sterilization by the mutant, which suggested that the mutant would be a potential for cost-effective commercial lactic acid production.

Mathematical modeling of lactic acid fermentation in bioreactor with carob extract

Abstract In this study, nonlinear sixteen mathematical models including Gompertz (G), generalized Gompertz (GG), modified Gompertz (MG), re-modified Gompertz (RMG), logistic (L), generalized logistic (GL), modified logistic (ML), re-modified logistic (RML), Richards (R), generalized Richards (GR), modified Richards (MR), re-modified Richards (RMR), Stannard (S), Baranyi (B), Weibull (W), and Morgan-Mercer-Flodin (MMF) were applied to fit cell growth, product formation, and sugar consumption of batch lactic acid (LA) fermentation in stirred tank bioreactor with carob extract. To determine the modeling success, root-mean-square-error (RMSE), mean-absolute-error (MAE), R2, slope, bias factor (BF), and accuracy factor (AF) were used. Results indicated that the best model for cell growth was MMF model (RMSE=0.24 g/L, MAE=0.16 g/L, R2=1.00, Slope=1.06, BF=1.04 and AF=1.16). For product formation, the best models selected were RMG (RMSE=1.33 g/L, MAE=1.00 g/L, R2=0.99, Slope=0.95, BF=0.94 and AF=1.11) and RMR (RMSE=1.33 g/L, MAE=1.01 g/L, R2=0.99, Slope=0.96, BF=0.94 and AF=1.12) models. As for sugar consumption, B model was the best model for estimation of experimental data (RMSE=0.88 g/L, MAE=0.52 g/L, R2=1.00, Slope=1.00, BF=1.00 and AF=1.01). Additionally, the most successful models that predict experimental kinetic data were GG, GL, S, and W models. Consequently, the best models selected could be used for more progress of LA production process in bioreactor with carob extract.

Parametric Optimization of Lactic Acid Production by Immobilized Lactobacillus casei Using Box-Behnken Design

Technological optimization of process parameters posses one of the open challenge for fermentative lactic acid (LA) production. Hence optimization of process parameters viz. sugar concentration, pH, biomass, incubation temperature and incubation time for maximizing fermentative lactic acid production from molasses sugar and corn steep liquor as a low cost carbon and nitrogen source, respectively by immobilized Lactobacillus casei MTCC 1423 cells has been carried out using Box Behnken Design (BBD). By applying multiple regressions on experimental data, quadratic models have been realized, explaining role of each variable and their quadratic interaction on LA production, LA productivity and yield coefficient. Analysis of variance has demonstrated that models are significant. The maximum LA production (132 g/(L fermentor volume) ), LA productivity of 2.36 g/(L×h) and yield coefficient of 0.936 g/(g substrate) have been estimated by the quadratic regression model for optimum process parameters values of sugar concentration (194 g/L), pH (6.85), biomass (310 mg, CDW), incubation temperature (37°C) and incubation time (57 h). The optimization validated experiments had resulted in LA production of 130±2.1 g/(L fermentor volume) ; LA productivity of 2.28±0.037 g/(L×h) and yield coefficient of 0.921±0.003 g/(g substrate) and which are substantially higher than those obtained with free cells of Lb. casei MTCC 1423 (2%, v/v inoculums size) at obtained optimized process parameters values. Thus resulted quadratic models provided an opportunity for scaling up the lactic acid production process and demonstrated the economic potential of using agro industrial waste molasses sugar for lactic acid production by Lb. casei MTCC 1423.

Techno-economic analysis of a food waste valorisation process for lactic acid, lactide and poly(lactic acid) production

Abstract A sustainable food waste valorisation process was proposed by designing a plant with a capacity of 10 metric tons (MT) hour−1 of food waste powder with a 20-year lifetime. Three scenarios were proposed with different products: Scenario I) lactic acid, Scenario II) lactide, Scenario, and III) poly(lactic acid) (PLA). Mass balance showed conversion yields of 3.1 MT of 80% lactic acid, 1.7 MT of lactide, and 1.3 MT of poly(lactic acid) from 10 MT of food waste powder. All scenarios were economically feasible, but Scenario I had the highest annual net profits (US$ 22,184,169), internal rate of return (31.1%), net present value (US$234,803,060) and the shortest payback period (5.1 years) at a discount rate of 5%. The minimum selling prices of lactic acid, lactide and poly(lactic acid) were US$943 MT−1, US$2073 MT−1 and US$3330 MT−1, respectively. Sensitivity analysis showed that the prices of lactic acid, lactide and poly(lactic acid) were the largest determinants of the profitability in the plant while the sale of by-products (animal feed) was also critical to the plant's economics. This work has cast insights on the techno-economic performance of a sustainable food waste treatment under a decentralised approach in urban areas.

Estimating the Limiting Rate of Dilution in Technology for Lactic Acid Production by Continuous Fermentation

The estimation of the dilution rate in a fermenter is associated with biotechnological features. The time of residence of the stream of substrates in the fermenter should ensure the growth of the microbial population. In other words, if the dilution rate D is higher or equal to the limiting value Dlim, synthesis has no time to take place and, as a consequence, no product (specifically lactic acid) is formed. In this study, as a result of mathematical modeling, the technological parameter D< Dlim has been calculated, which ensures real conditions for the practical implementation of the continuous process of lactic acid production.

Scaling-up of simultaneous saccharification and fermentation of lactic acid from microwave-alkali-treated empty fruit bunches

The goal of this work was to scale up the simultaneous saccharification and fermentation (SSF) of lactic acid using microwave-alkali-pretreated empty fruit bunches (EFB) from a scale of 16 L to a scale of 150 L. To facilitate the scaling-up process of lactic acid production by Rhizopus oryzae NRRL 395, a scaling-up criterion of constant kLa value was applied. Operating conditions, such as aeration rate and superficial velocity, were varied and evaluated on both scales (16-L and 150-L). The highest lactic acid yield of 6.8 g/L was obtained under an operating condition of 1 vvm (0.061 s-1). Parallel aeration rates were determined for the 150-L fermenter system to obtain the same kLa value as the 16-L fermenter. An operational condition of 0.5 vvm dissolved oxygen supply in the 150-L fermenter was optimal to support an identical value of kLa and production rate of lactic acid for both scales.

Mathematical modeling of biotechnological process of lactic acid production by batch fermentation: A review

The results of analyzing mathematical models of the process of batch fermentation for the production of lactic acid have been presented. Three groups of mathematical models have been considered. The first two groups are based exclusively on the notion of the specific growth rate, dependent or independent on substrate concentration. The third group uses the notions of the specific rate of substrate consumption and specific rate of product formation in additions to the notion of specific growth rate. The numeric estimates of constants are presented for the majority of models as well as comparison with the experimental studies. Mathematical models of the processes where the formation of side products is possible have been discussed, which may or may not be of value on their own. The possible practical applicability of the models has been evaluated based on the results of the analysis.