Formulace fyzikálně-chemických problémů

S prudkým rozvojem techniky počítačů roste i snaha převést na ně práci při řešení úloh z praxe, využít jejich rychlosti a výkonnosti. Toto dění se však neobejde bez účinných algoritmů řešení a bez odborníka, který je schopen dávat příslušné pokyny počítači. Proto je nutné snažit se o co nejlepší formulaci řešených problémů a zvyšovat úroveň a znalosti matematického modelování, numerických metod, počítačových programů a jazyků. Matematické modelování s využitím počítačů je v současné době jedním z nejaktuálnějších a nejzákladnějších aspektů vědy a techniky. Tento předmět by měl studentům pomoci vyznat se v problematice popisu, výběru a užití již známých metod numerické matematiky v některých kapitolách fyzikální chemie. Nepůjde o to vymýšlet nové algoritmy výpočtů, ale snažit se pochopit podstatu problému, umět ho sofistikovaně formulovat a popsat známými matematickými postupy. Z bohatých knihoven programů je pak možné vybírat vhodný postup k co nejrychlejšímu získání kvalitních výsledků. V první části této studijní literatury se budeme zabývat numerickým řešením základních analytických matematických úloh, a to řešením algebraických a transcendentních rovnic, řešením soustav lineárních a nelineárních rovnic, interpolací, numerickou derivací a integrací a numerickým řešením obyčejných diferenciálních rovnic. Ve druhé části bude na konkrétních úlohách ukázána pokud možno komplexní formulace problému, tzn. myšlenková stavba modelu na základě fyzikální skutečnosti, matematický popis modelu, zjednodušování eventuálně zobecňování. Ve třetí části bude pomocí několika numerických matematických metod hledáno řešení konkrétních úloh včetně stanovení parametrů modelu pomocí lineární a nelineární regrese, vícenásobné lineární regrese, pomocí optimalizačních postupů přímohledajících a derivačních metod apod. V poslední části na vzorových experimentálně naměřených problémech bude pomocí výpočetní techniky zpracováno několik konkrétních úloh z fyzikální chemie – reakční kinetiky

Determination of the temperature dependence of the density of rapeseed oil and rape methyl ester (biodiesel) by the method of volume expansion

Simple methods and apparatus for determination of the density of liquids at variable temperatures were developed. Their correct function was demonstrated by the comparison of the literature and experimental data for ethanol. The temperature dependences of the density of crude rape seed oil and of rape seed oil-ethyl ester (bio-diesel) were measured in the interval of 15–70 °C. The precision of the method described is better than ± 0.5 mg cm−3 at the temperature tolerance ± 0.1 °C

Treatment of glycerol phase formed by biodiesel production

Glycerol is a by-product of biodiesel produced by transesterification and is contained in the glycerol phase together with many other materials such as soaps, remaining catalyst, water, and esters formed during the process. The content of glycerol is approximately 30-60 wt.%. In this paper, treatments of the glycerol phase to obtain glycerol with a purity of 86 wt.% (without distillation) and a mixture of fatty acids with esters (1:1) or only a mixture of fatty acids with a purity of 99 wt% are presented. The treatment was carried out by removing of alkaline substances and esters. Fatty acids were produced by saponification of the remaining esters and subsequent neutralization of alkaline substances by phosphoric, sulfuric, hydrochloric or acetic acids. Salts are by-products and, in the case of phosphoric acid can be used as potash-phosphate fertilizer. The process of treatment is easy and environmentally friendly, because no special chemicals or equipment are required and all products are utilizable

Relationship of variables affecting separation following transesterification of vegetable oil

The transesterification of vegetable oils (rapeseed and sunflower oils were used) by low molecular alcohol is the most used method of biodiesel production. A heterogeneous reaction mixture is formed by transesterification containing ester and glycerol phases. Biodiesel is gained by the sedimentation of this mixture. We have studied how separation conditions (independent variables: amount of added water, intensity and time of stirring, etc.) affect the quantity and the quality of both phases (dependent variables). The reaction mixture presents a multivariable system, therefore the statistic method Plackett - Burman was used in the planning of experiments. The multidimensional linear regression was used for the description of the relationship between independent and dependent variables. The mathematical model describing this relationship was created for both types of oil

The Factors affecting the separation of the reaction mixture after transesterification of rapeseed oil

The most used method of biodiesel production is the transesterification of vegetable oils by basic homogeneous catalyst. Heterogeneous reaction mixture is formed by this process and contains two phases: ester phase and glycerol phase. From this mixture, biodiesel is gained by sedimentation. Quality and quantity of both phases are affected by conditions of sedimentation process. It was studied how conditions (independent variables: temperature of separation, amount of added water, time of sedimentation, etc.) affect the quantity and the quality of both phases (dependent variables). The statistic system Plackett - Burman was used for experiments planning. The relationship between independent and dependent variables was found and described by multidimensional linear regression. The created model allows to calculate the optimum conditions of biodiesel production so the quality of biodiesel fills the EN 14214

Biodiesel preparation in a batch emulsification reactor

The transesterification of vegetable oils (rapeseed oil was used) by low molecular alcohol is the most used method of biodiesel production. Since the reaction proceeds at the alcohol-oil interface, it is necessary to create a large interphase surface area using a special emulgation attachment. It was studied how the conditions (independent variables: molar ratio alcohol to oil, amount of used catalyst – KOH, time and temperature of reaction, intensity of stirring, revolution of emulgation attachment) affected the quality and quantity (dependent variables) of the ester phase – biodiesel. The amount of used catalyst was calculated with respect to the content of free fatty acid in oil. The statistical system of Plackett-Burman was used for experiment planning. Relationship between independent and dependent variables was found and described by multidimensional linear regression. Various statistical tests (principal component analysis, correlation matrix) were carried out, also

Relationships among flash point, carbon residue, viscosity and some impurities in biodiesel after ethanolysis of rapeseed oil

Many samples of rapeseed oil ethyl ester were prepared by alkaline-catalyzed transesterification at various conditions (reaction time, temperature, amount of catalyst, the molar ratio of ethanol to oil, the rotations of a disperser and the purification by water). The concentrations of the key impurities for biodiesel quality (the concentrations of monoglycerides, diglycerides, triglycerides, free glycerol, ethanol, free fatty acids, water) and some qualitative parameters (flash point, carbon residue, kinematics viscosity at 40 °C) were determined and then the relationships among them were found out. The relationships were characterized by the linear or non-linear statistical models. The found models enable the better understanding of the significance of the qualitative parameters and estimate them from the concentrations of impurities. The temperature dependence was also measured in the case of the viscosity of ethyl ester and used rapeseed oil

Ethanolysis of rapeseed oil - Distribution of ethyl esters, glycerides and glycerol between ester and glycerol phases

The distribution of ethyl esters, triglycerides, diglycerides, monoglycerides and glycerol between the ester and glycerol phase was investigated after the ethanolysis of rapeseed oil at various reaction conditions. The determination of these substances in the ester and glycerol phases was carried out by the GC method. The amount of ethyl esters in the glycerol phase was unexpectedly high and therefore the possibility of the reduction of this amount was investigated. The distribution coefficients and the weight distributions of each investigated substance were calculated and compared mutually. The distribution coefficients between the ester and glycerol phase increase in this sequence: glycerol, monoglycerides, diglycerides, ethyl esters and triglycerides. Soaps and monoglycerides in the reaction mixture cause a worse separation of ethyl esters from the reaction mixture. The existence of a non-separable reaction mixture was observed also, and its composition was determined

Sedimentation analysis in liquid-liquid system applied to biodiesel production research. introducing mathematical models

This work is focused on description of gravitation separation process of the ester phase from the glycerol phase for biodiesel production. Four mathematical models describing separation were created. Two independent methods were used for monitoring of separation: the first method is based on the determination of the time dependence of the actual amount of the glycerol phase on the bottom of a sedimenting vessel by digital camera records. The second one measures light absorption changes caused by the lowering of the glycerol phase during the sedimentation. The obtained data was curve fitted by developed mathematical models, which are (i) based on Stokes equation and proposed distribution function, (ii) based on analogy to reaction kinetics. The distribution function has several simplified presumptions, e.g., interactions are neglected, the function has one peak. The obtained model parameters (from the curve fitting) can be consequently used for the quantification and the prediction of sedimentation behaviour such as the sedimentation conditions, the size of settling devices and the evaluation of dependences on raw material quality