Mathematical modeling of the kinetics of binder hardening

The paper intends to point out some methodological aspects to treat the difficult problem of mathematical modeling of concrete taking care of the main factors influencing the process. It will be demonstrated that the information coming from the physico-chemical phenomena like dissolution, nucleation, crystallisation etc. and the corresponding evolution of state, recognized by an adequate output of a measurement, can be reflected in a more or less realistic way. The investigation is done to have the necessary background to describe the changing properties of concrete under computer aided production control as well as to give a new insight in the outgrowth of variation in the composition of the system.     

Mathematical simulation of the combustion of slurry fuels

A mathematical model is proposed for the combustion of slurry fuels in the quasi-one-dimensional approximation. A numerical simulation is made of combustion of a slurry based on carbon and toluene in a combustion chamber and in a nozzle. The completeness of the combustion of the slurry is found to depend strongly on the excess oxidant ratio α_ox with maximum for α_ox ≈ 1. Scientific-Industrial Firm “State Institute of Applied Chemistry,” 197198 St. Petersburg. Translated from Fizika Goreniya i Vzyrva, Vol. 31, No. 6, pp. 41–48, November–December, 1995.     

Mathematical simulation of the hydrogenation of borodino coal

The kinetic and thermodynamic parameters of the hydrogenation of Borodino brown coal were calculated. With the use of equilibrium-kinetic analysis, the second-order reaction rate constants of forward and reverse reactions, the equilibrium constant, the activation energy, and the thermal effects of brown coal hydrogenation reactions were determined in a temperature range of 648–698 K at a hydrogen pressure of 10 MPa. In the course of the study, it was found that the experimental data are indicative of the adequacy of the equilibrium-kinetic analysis model for second-order reactions.     

The simulation of precipitation kinetics

The kinetics of precipitation is formulated as a set of rate equations typical of chemical mechanisms in which initiation of monomer and propagation due to homogeneous and heterogeneous nucleation are included. This model discrete in aggregate size is then transformed into a continuous one so that an efficient numerical solution may be obtained via a weighted residual technique. The resulting model consists of a set of ordinary differential equations with coefficients defined in terms of integrals for the moments of the particle size distribution and is best solved by an implicit method.     

乙烯氧化反应器数学模拟

针对扬子石化公司乙烯氧化制环氧乙烷工业规模的壁冷式固定床反应器,在YS-6型银催化剂宏观动力学模型的基础上加以修正,获得了YS-7型银催化剂宏观动力学模型,建立了环氧乙烷合成固定床反应器的一维拟均相模型,通过模型计算值与工业生产实际值的比较,两者相差很小,验证了反应器模型和所用的宏观动力学模型的准确性,可用作扬子石化公司环氧乙烷合成反应器的模拟与操作优化。     

Mathematical simulation of an oilseed press

A mathematical model of an oilseed press was developed by superimposition of filtration analysis on screw extrusion theory to calculate press throughput and residual oil content in presscake for a given press geometry and physical properties of oilseed. The model predicted that press performance would improve, i.e., the throughput would increase and residual oil would decrease, if the press were cooled during operation. Longer presses would also give higher throughputs with lower residual oil contents. The predicted effects of changes in shaft speed and choke opening on press performance agreed reasonably well with experimental results obtained on a small laboratory press. A relatively large error of 9.0% in the prediction of throughput could be attributed to changes in viscosity of oilseed mass occurring during its passage through the press. It is expected that use of ‘expression’ analysis in place of the simple filtration analysis would improve the predictive ability of the model.     

Mathematical simulation of the thermal stability of magnesium oxide

A simulation of the behavior of nonporous single-crystal magnesium oxide under conditions of heat loading that approach the operating conditions of casting ladles in ferrous metallurgy is performed by means of mathematical methods. Both numerical and analytic methods are used for the calculations. The temperature and mechanical stress fields and such breakdown parameters of materials as the moment of appearance of cracks, the thermal stability criterion (breakdown temperature drop of surface of material), etc. were determined as a result of the calculations. Results of calculations are presented and an analysis of the application of mathematical methods to the simulation of different heat treatment regimes of a material is performed.     

Mathematical simulation of the viscous properties of concentrated suspensions

A mathematical model for calculating the viscous properties of concentrated suspensions characterized by particle sizes of 30 to 800 µm), solids volume fractions of 1 to 70 vol %, different particle-size distributions, and a shear-rate range of 0.16 to 437 s^?1, which can describe the time evolution of the properties, is proposed. The model can be applied to calculating the viscous properties of catalyst oxide pastes, particulate-filled polymeric pastes, and the like.     

半间歇搅拌釜式乙氧基化反应器的数学模拟

以KOH催化条件下乙二醇乙氧基化为例,建立了工业规模的、同时考虑动力学、气液平衡、气液传质、反应体积变化和惰性气体氮气影响等的半间歇搅拌釜式乙氧基化反应器的数学模型。通过数学模拟考察了环氧乙烷进料速率对反应器操作的影响,得到安全限制下适宜的环氧乙烷进料速率。在此基础上,模拟得到反应器中压力、环氧乙烷在气液相中的组成及乙氧基化产物随时间的分布,并同工业试验数据进行了比较。结果表明了模型的可靠性。     

Mathematical modeling of chain-end scission using continuous distribution kinetics

Mathematical models that use continuous distributions to represent reacting polymer populations have been highly successful, and the method of moments is often used as a convenient means for obtaining solutions for the properties of the polymer population over time. However, there has been some controversy regarding the application of the method of moments for polymer degradation by chain-end scission. Here, we provide a rigorous treatment of chain-end scission using a continuous distribution for the polymer population and show that the method of moments has shortcomings for general use. As an alternative to the method of moments, we propose a solution method in which the continuous distribution is mapped to a set of discretized points, and the time-evolution of the distribution is obtained at the grid points. The results using this method are shown to agree well with the solution to the discrete model. The method is particularly well-suited for solving problems involving broadly distributed populations that are often found in nature.     

树枝状大分子对原油的破乳与降粘作用

采用发散法合成以乙二胺为核的聚酰胺-胺树枝状大分子,针对O/W型的模拟原油乳液评价了PAMAM的破乳性能,同时评价了PAMAM对稠油的降粘性能。结果表明,整代PAMAM均具有一定的破乳效果,其中3.0代PAMAM在45℃、添加量为100mg.L-1,破乳时间为60min时,破乳率达80%。半代PAMAM均具有一定的降粘效果,在70℃,添加量为0.6%,降粘时间为60min时,2.5代的降粘率为28.2%。     

油砂沥青超声波减粘工艺研究

油砂沥青粘度较大,自然状态下不易流动,严重影响了管道输送及加工,针对目前油砂沥青研究中存在的问题,采用超声波进行了减粘的实验研究。实验综合考察了超声波作用时间、温度、超声波频率、超声波功率等因素对减粘效果的影响。实验结果表明,在适当的超声作用时间(20 min)、适宜的温度(30℃)、适宜的超声波频率(20 kHz)和超声波功率(250 W)的条件下,油砂沥青的减粘率可达80%以上。经超声波处理后的油砂沥青粘度略有恢复,但仍远低于处理前的粘度,超声波减粘效果良好。     

Mathematical simulation of the lagrange ballistic problem for high-velocity systems

The problem of a piston being pushed by expanding gases released during rapid burnup of a charge is simulated mathematically. The model includes the laws of conservation of the dynamics of a two-phase medium, supplemented by the equation of kinetics with a linear dependence of the combustion rate on the pressure. The results of calculations for three types of ballistic systems showed good agreement with experimental data. Analysis of the calculations indicated that the complete gasdynamic picture must be taken into account when the projection velocity is increased and that the simplified models used earlier are inapplicable. Institute of Chemical Physics, Russian Academy of Sciences, Chernogolovka 142432. Translated from Fizika Goreniya i Vzyyrva, Vol. 30, No. 5, pp. 71–78, September–October, 1994.     

Viscosity modification of flash pyrolysis tars

A study was made of the effect of a number of additives on the viscosity of a characteristic tar produced by the flash pyrolysis of indigenous Australian coals. The results indicate that aliphatic compounds are more effective than aromatic compounds in lowering the viscosity. This observation is of significance in the selection of suitable recycle solvents and the dissolution of aged tars.     

Characterization of pyrolysis tars from Canadian coals

Tars produced by rapid pyrolysis of several Canadian coals have been characterized. Raw tars were separated into solvent fractions which were analysed by a combination of PONA separation by high-performance liquid chromatography, high-resolution capillary gas chromatography and chromatography-mass spectrometry. The alkane-alkene pairs and poly nuclear aromatics found in hexane and benzene fractions are reported for four coals pyrolysed under a range of conditions. The predominance of C₈ to C_14–18 alkane-alkene pairs together with alkyl-substituted benzenes and naphthalenes in the hexane-soluble oils, and three-to five-membered ring aromatics in the benzene-soluble asphaltenes from bituminous coal tars was established. Effects of pyrolysis temperature on aromatic homologues and key nitrogen, sulphur and oxygen heterocyclic homologues are shown.     

Mathematical models for kinetics of batchwise hydrogenation of shale oil

Hydrogenation of shale oil in a batch autoclave is described by a second order kinetic equation depending on the hydrogen current concentration (H) and on the current value of a total characteristic of the oil (x_i), both approaching to their equilibrium levels (H_∞, x_i∞). Algorithms are proposed to estimate the values of hydrogenation rate coefficient (k) and H_∞ from the plot of decrease in hydrogen concentration in time versus H at isothermal conditions. A new concept “specific change of the characteristic” (β_i = dx_i / dH) is introduced to handle various x_i (oil yield, viscosity, density, iodine number, and yield of the fraction 200–275 °C).The equilibrium constants (K_i) and β_i for the characteristics are estimated on the basis of experimental results. The temperature-dependencies for k, K_i and β_i are determined. A scheme is proposed to predict current values of H and x_i for different H₀, T_max and oil mass under isothermal and non-isothermal conditions.The model deduced and the coefficients and constants found can be applied for quantitative evaluation of catalysts and initial oils for hydrogenation.     

Matlab用于葡萄糖加氢催化反应动态模拟

对用于葡萄糖催化加氢反应的钌碳催化剂的催化反应数据进行分析和曲线拟合。用Matlab进行计算机模拟实验,找出比表面积和孔容对催化反应的转化率和选择性影响的最优条件,预测最佳催化反应选择性和反应转化率区间,优化筛选催化剂载体的条件,以改进催化剂的活性。     

Mathematical simulation of lysine dendrimers: Temperature dependences

The mathematical simulation of second- and fourth-generation lysine dendrimers is performed via the molecular-dynamics method. Temperature dependences of primary structural characteristics are obtained. It is shown that the sizes and atomic distributions of these dendrimers are weakly temperature-dependent. Together with the structural properties, the local mobility of CH₂ groups in the dendrimers is investigated via the molecular-dynamics method and NMR spectroscopy. It is shown that the orientational mobility of internal groups of the lysine dendrimers is lower than that of terminal groups, in agreement with the data available for flexible-chain dendrimers. Changes in correlation times with temperature are well described by the Arrhenius dependence. At the same time, the orientational mobility of internal groups in the lysine dendrimers depends on the generation number. This behavior is different from that of flexible-chain dendrimers, in which the mobility of internal groups is the same for dendrimers of different generations.     

Mathematical models of fermentations and a simulation of the griseofulvin fermentation

A number of models which have recently appeared in the microbiological literature are described and discussed. A simulation of the griseofulvin fermentation is also reported. Models described range from simple models involving curve-generating equations providing parameters which describe fermentation phenomena adequately for optimisation purposes, to more elaborate mechanistic models which involve the quantity of substrate required to produce cells and products. Beyond this are complex models capable of describing biochemical mechanisms and able to elucidate a fermentation at a deeper level. The construction of the model for griseofulvin fermentation and its comparison with actual results have shown how a model can bring to light new ideas about the way fermentations behave and point to the most useful areas of investigational work.