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Документ Development of the mathematical model of the kinetics of the stationary process of bio-cleaning with substratic inhibition(Scientific Route OU, 2018) Bakharieva, Ganna; Petrov, Serhii; Falalieieva, TetianaA scientifically sound method for calculating the parameters of bio-cleaning should contain as a basic a reliable mathematical description of the stationary process. The results of stationary laboratory experiments are presented in the coordinates “specific rate of destruction V – concentration ρ”. Statistical processing proves the presence of substrate inhibition for both gaseous and soluble and dissolved harmful substances in water. For an analytical description of the dependence of the biooxidation rate on the concentration of contaminants, a phenomenological approach is applied, taking into account in a simple form two obvious phenomena: the contact of a microorganism with a substrate molecule and the inhibitory effect of the medium on it. The numerical values of empirical dependency coefficients for the studied processes are calculated. A differential equation is proposed at the macro level that describes the kinetics of biochemical destruction. The concept of a macrokinetic mathematical model of bioremediation is defined as a system of two functions that quantitatively reflect the dependence of the specific oxidation rate of pollution on its concentration and concentration on time, as well as satisfying the relationship between the relationships of the same parameters in differential form. The dependence of concentration on time is defined both in the form of a numerical integration algorithm and in the form of an approximate formula. The adequacy and universality of the proposed model for the studied processes is proved. The advantage of the proposed model of substrate inhibition kinetics is the simplicity of the structure of the basic formula and the ease of determining empirical coefficients based on this. In addition to numerical integration for determining the time of destruction, an approximate analytical solution is found, which can be adequately used in the concentration range of the experimental study. Further research is aimed at developing methods for calculating non-stationary processes in biochemical purification plants of certain specific types.Документ Construction of a generalized model of the harmful substances biochemical destruction process kinetics under conditions of substrate inhibition using the methods of simulation modeling(Технологический центр, 2019) Bakharieva, Ganna ; Falalieieva, Tetiana; Petrov, Serhii; Mezentseva, Iryna; Kobylianskyi, Borys; Tolkunov, Ihor; Bondarenko, OleksandrFor the purpose of obtaining the complete range of solutions for substrate inhibition of varying intensity, the mechanism of enzyme kinetics in a biocell was modeled by a multi-channel queuing system. A full range of solutions is required to make a well-grounded choice of a unified generalizing formula. The process of biodegradation with substrate inhibition was described mathematically using the method of dynamics of averages. For specific destruction rate, a full range of solutions Vn of the system from minimum n=2 to limiting n→∞ order was found. It was established that the parameters of the curve shape for the solution with minimum inhibition intensity V2 substantially stand out from the general series of the spectrum formulas. The value of the coordinate of function maximum (n=2) V2 is by 1.42 times higher than that of dependence (n=3) V3. In the numerical experiment, the physical test was simulated by description with the help of the method of the least squares of the data, assigned by the calculation from the formulas of different structures, bearing in mind a sporadic random error. The series of numerical experiments demonstrated the capability of the formula of limiting order formula Ve to describe the dependences of the whole spectrum of solutions. During describing the intermediate ratio V3 with the help of formulas V2 and Ve, the benefit is the possible range of changing the concentrations, which is by 1.5-2 times larger at the same relative error for dependence Vе. For critical minimal order, an average relative error is sure not to exceed five percent. An increase in random error always result in statistical equality, in accuracy of describing by formulas of minimal V2 and limiting orders Ve of the data, assigned by calculation of second-order dependences. Statistical equality is achieved at the ratio of a random error to the initial error equal to ≥2.4. Collectively, the importance of the results of numerical modeling of a physical experiment involves proving the possibility of using the formula of limiting order Ve as unified when describing the biodegradation processes with different mechanisms of substrate inhibition. This conclusion is proved by the adequate (R2=0.9396-0.9953) description with the help of the dependence of limiting order of experimental data on five harmful substances with varying inhibition degrees. A large amount of calculation allowed achieving a definite result – we obtained the unified formula that makes it possible to proceed to scientifically grounded design calculations for bio-treatment plants.