Modified Shrinking Core Model for Reversible Sorption on Ion-Exchange Resins

Abstract

A modified shrinking core model is proposed to correlate dynamics of acid sorption on weak base ion-exchange resins in free base form. The model considers reversibility of the sorption process which is ignored in the conventional shrinking core model. The model is easy to apply and is shown to yield results which are in agreement with a computationally intensive rigorous model. The model is successfully verified using the experimental data on sorption of strong acids (HCl and HNO₃) on weak base resins (Dowex WGR-2 and Amberlite IRA-93).     

Shrinking Core Model in characterizing aqueous phase dye adsorption

The fluid-solid non-catalytic reactive system is characterized by the widely accepted Shrinking Core Model. In the present investigation the same model has been applied to characterize the adsorption of Methylene Blue (MB) and Congo Red (CR) dyes in the aqueous phase onto Rice Husk Ash (RHA). The effective pore diffusivities of different dye molecules in RHA are determined by a suitable global optimization technique. The depth of penetration has also been estimated for various initial concentrations of dyes. The values predicted by the model are compared with experimental concentration profiles at different initial concentrations of these dyes. The theory-experiment comparison has revealed that predicted values are in excellent agreement with the experimental values.     

A 1-D non-isothermal dynamic model for the thermal decomposition of a gibbsite particle

A 1-D mathematical model describing the thermal decomposition, or calcination, of a single gibbsite particle to alumina has been developed and validated against literature data. A dynamic, spatially distributed, mass and energy balance model enables the prediction of the evolution of chemical composition and temperature as a function of radial position inside a particle. In the thermal decomposition of gibbsite, water vapour is formed and the internal water vapour pressure plays a significant role in determining the rate of gibbsite dehydration. A thermal decomposition rate equation, developed by closely matching experimental data reported previously in the literature, assumes a reaction order of 1 with respect to gibbsite concentration, and an order of −1 with respect to water vapour pressure. Estimated values of the transformation kinetic parameters were k₀ = 2.5 × 10¹³ mol/(m³ s) for the pre-exponential factor, and E_a = 131 kJ/mol for the activation energy. Using these kinetic parameters, the gibbsite particle model is solved numerically to predict the evolution of the internal water vapour pressure, temperature and gibbsite concentration. The model prediction was shown to be very sensitive to the values of heat transfer coefficient, effective diffusivity, particle size and external pressure, but relatively less sensitive to the mass transfer coefficient and particle thermal conductivity. The predicted profile of the water vapour pressure inside the particle helps explain some phenomena observed in practice, including particle breakage and formation of a boehmite phase.     

Effect of Calcination Conditions on Crystalline Structure and Pore Size Distribution for a Mesoporous Alumina

In this article, a mesoporous commercial alumina was calcined in the temperature range of 600°C–1200°C. The effect of several parameters such as calcination temperature, calcination time, heating rate, and calcination steps on phase transformation and crystal size was experimentally investigated. The characterization of the commercial mesoporous alumina and samples calcined at 1000°C, 1040°C, 1070°C, 1100°C, and 1200°C by single-step and multi-step calcination was performed using XRD and N₂ adsorption/desorption techniques. For the commercial mesoporous alumina, TG/DTA analysis was also performed. Experimental results showed that mostly pure α-Al₂O₃ was obtained at 1100°C.     

水泥煅烧工段机理分析与神经网络预测方法

采用神经网络的方法建立水泥预分解窑煅烧工段的预测模型。选择合理的状态与控制变量,通过采集实际运行数据来训练神经网络。构建的基于BPNN神经网络的煅烧预测模型能够较好地拟合采样数据,具有较好的泛化能力。     

A Quasi‐Steady State Shell and Shrinking Core Approach to the Drying of Porous Particles and an Example of Parameter Identification

A quasi‐steady state shell and shrinking core approach which recognizes heat and mass transfer resistances in both the gas and particle phases for drying of a porous particle is proposed. A mean field model (constant properties) using this approach was embedded in a spreadsheet combined with a genetic algorithm for parameter identification to provide an easy means of characterizing the drying process from drying data. In drying, assuming a mean field, four major parameters are typically unknown: two related to the process (heat and mass transfer coefficients) and two which incorporate porous particle properties (shell thermal conductivity and vapour diffusivity). It is shown how these four parameters may be determined from experimental drying data. The model was applied to data for spouted bed drying of rice. For the particular case studied, external heat transfer was found to be the controlling mode, although resistance to moisture diffusion within the particle is important. The approach presented admits of future refinements to improve its scope and utility.     

Vapor recovery reactor in carbothermic aluminum production: model verification and sensitivity study for a fixed bed column

In this paper we develop a distributed parameter model for a fixed bed vapor recovery reactor (VRR) in a carbothermic aluminum process. The model we develop for the reaction mechanism is based on the mass transfer limited (shrinking core) reaction scheme. This model is combined with the partial differential equations (PDEs) describing the component mass and energy balances. The system of PDEs is converted to a large system of differential algebraic equations (DAEs) using the method of lines. The large scale system of DAEs is solved using a DAE solver. The theoretical results have been compared to experiments, showing that the model predicts the reactor's behavior. Sensitivity analysis has been applied to the model using two important variables, gas superficial velocity and gas composition.     

H2S在颗粒脱硫剂上反应的动力学性能

以自制含３０％Ｋ２ＣＯ３的固体脱硫剂在２０℃常压下分离Ｎ２－Ｈ２Ｓ气体混合物,Ｈ２Ｓ与柱形颗粒固体中的Ｋ２ＣＯ３反应的动力学性能。在灰层扩散控制区,由核收缩模型得到的方程：Ｋｔ＝（１－ｘ）ｌｎ（１－ｘ）＋ｘ能很好地描述实验数据,并由此得到了Ｈ２Ｓ的颗粒灰层内的有效扩散系数。发现在低浓度条件下,Ｈ２Ｓ在灰层内的有效扩散系数与其浓度无关。     

冶金过程多组分体系同时反应的动力学模型及应用

将钢铁冶金中的多组分同时反应作为一个综合的反应体系进行研究,考虑其中各反应间的影响. 根据冶金热力学和动力学原理建立多组分渣-金-气反应体系同时反应动力学模型,编制计算程序,得出成分对时间的变化曲线,并用含Fe-Cr-Mn-C的渣-金反应体系的实验进行了验证. 结果表明,金属液中C和Mn组分的计算浓度与实测值基本吻合,Cr的计算浓度与实测值的相对误差在9.1%以内. 在直流电弧下熔炼存在大气通过渣层向金属液的传氧现象,其数值与大气向钢液直接传氧的数值相同. 采用模型方法能较好地解释过程中的反应现象,揭示过程的机理.     

Model for coal oxidation kinetics. 2. An effectiveness factor interpretation

Rate expressions are developed to describe the oxidation of coal in a fixed-bed reactor under conditions of significant diffusional effects. The model defines individual effectiveness factors for carbonic gas formation, oxygen deposition, and water production, to modify a chemical model derived previously. Experiments carried out on seven coals ranging in rank from lignite to bituminous to anthracite. All the coals exhibited particle size effects and the results fit the model in most cases to within ±10% both in the rate of overall oxidation and with respect to the individual reaction rates for several products. Activation energies and effectiveness factors were obtained for each coal and for each reaction. The effluent gas $\text{CO}{}_2\text{CO}$ ratio was found to be virtually constant for all five bituminous coals, being independent of reaction temperature, coal particle size, and oxygen partial pressure.     

由氟化锂和五氯化磷制备五氟化磷的动力学研究

在150~195 ℃下,研究了氟化锂和五氯化磷制备五氟化磷的反应过程,并应用缩芯模型处理数据,确定了反应的动力学模型：反应初期（0～0.5 h）,该反应受化学反应控制,动力学方程为k_s=22.2exp[-34 490/(R_gT)];反应后期（1～3 h）,该反应主要受内扩散控制,动力学方程为D_e=4.357×10^-7exp[-29 980/(R_gT)]。该研究旨在揭示氟化锂和五氯化磷制备五氟化磷反应过程的相关规律,为工业生产五氟化磷提供必要的基础数据。     

流化床化学反应器的气固两相模型计算与结果讨论

针对流化床化学反应器的PF－PF两相模型,采用四阶龙格－库塔算法,就一级反应对气泡相和密相之间的质量平衡方程进行精确求解,并与近似解（密相学梯度变化为零）进行了比较;得出流化的最佳操作条件。     

Mathematical model for lactic acid production from lactose in batch culture: Model development and simulation

The models available to describe lactic acid production do not seem to fit the experimental data very well, especially at the end of batch cultures. From a careful analysis of batch data, an unstructured model of the process has been derived, in which the specific growth rate variations and lactic acid concentration with time have been described by complemented logistic functions. Also, an additional term has been introduced into the Luedeking–Piret expression, taking into account the reduction in rate of lactic acid production observed at very low growth rate.     

Analysis of the kinetics of growth and lactic acid production for Lactobacillus helveticus growing on supplemented whey permeate

Growth of Lactobacillus helveticus on supplemented whey permeate was divided into five phases: lag, exponential, deceleration, stationary and decline phases. Each phase was characterized by simple model kinetics. From this and by considering a partial association of lactic acid production with growth, with an additional term introduced to account for cessation of production when the carbon substrate became limiting, the lactic acid production was analytically deduced for each growth phase. For both growth and production data, on the whole culture, the calculated values were found to match experimental data. All the model parameters can be easily deduced from experimental data. The model allows therefore a fine analysis of growth and production kinetics. Copyright © 2005 Society of Chemical Industry     

Development of a mathematical model for Bacillus circulans growth and alkaline protease production kinetics

BACKGROUND: An unstructured mathematical model was developed to understand information on the relationship between Bacillus circulans growth and metabolism‐related protease production (using logistic and Luedeking–Piret equations respectively) in a batch reactor with respect to glucose consumption and fermentation time. The objective was to develop an indispensable tool for the optimisation, control, design and analysis of alkaline protease production. RESULTS: Biomass growth and enzyme production titres changed with a change in substrate concentration. Modelling analysis of biomass and enzyme production titres at different substrate concentrations revealed significant accuracy in terms of statistical consistency and robustness with respect to fermentation kinetic profiles. CONCLUSION: With the B. circulans strain used, an economic protease yield (2837 × 10³ U g^?1) with respect to biomass and glucose ratio was achieved at low substrate concentration (10 g L^?1). The developed model could be effectively utilised for designing, controlling and up‐scaling the protease production process in high‐density fermentation in selected bioreactors with statistical consistency. Copyright © 2008 Society of Chemical Industry     

灰色-马尔可夫的改进模型及在陶瓷工业产值预测

灰色模型是经济预测方法中最有效的方法之一,但灰色模型对波动性大的序列预测时精度较差.针对这一不足,提出灰色—马尔可夫的改进模型.新模型将原始序列进行对数运算提高数据光滑度,采用距离法降低灰色模型的相对误差,马尔可夫链对预测值进一步修正.将改进模型运用到景德镇陶瓷工业产值预测中,并与传统灰色模型、灰色-马尔可夫模型预测结果进行对比.结果表明改进模型的相对误差远小于灰色模型,预测精度优于灰色-马尔可夫模型,更能反应经济发展趋势.     

基于产教融合的会计专业中高职衔接“3+X+2”人才培养模式研究

随着“大数据”“互联网+”等信息化技术的进步,数据集中化处理、财务共享中心的建立逐渐替代模式化的人工处理,单纯以培养传统基础核算型会计人员的中职教育模式已经难于独立承担高素质技术技能会计人才培养的重任,在分析会计专业中高职衔接“3+2”人才培养模式存在问题的基础上,提出中高职衔接“3+X+2”人才培养模式实施建议,以实现职业教育资源统筹优化,中高职教育有效衔接。     

多层压电陶瓷变压器等效电路模型及其特性研究

提出了一种新颖的多层压电陶瓷变压器等效电路模型和分析方法。基于多层压电变压器陶瓷片在结构上的电学并联关系，建立了其在电路上的并联表示模型，并把输出电量与输入电量之间的关系用矩阵形式表达，简化了分析过程，为压电变压器的设计提供了一种通用而简单的分析方法。仿真结果验证了该方法的有效性，获得了良好的输入阻抗特性和升压比特性，升压比约为1200。     

An Ovine Model for Percutaneous Pulmonary Artery Laser Denervation: Perivascular Innervation and Ablation Lesion Characteristics

Background: Pulmonary artery denervation (PADN) is an evolving interventional procedure capable to reduce pulmonary artery (PA) pressure. We aimed to compare PA nerve distribution in different specimens and assess the feasibility of an ovine model for a denervation procedure and evaluate the acute changes induced by laser energy. Methods: The experiment was divided into two phases: (1) the analysis of PA nerve distribution in sheep, pigs, and humans using histological and immunochemical methods; (2) fiberoptic PADN in sheep and postmortem laser lesion characteristics. Results: PA nerve density and distribution in sheep differ from humans, although pigs and sheep share similar characteristics, nerve fibers are observed in the media layer, adventitia, and perivascular tissue in sheep. Necrosis of the intima and focal hemorrhages within the media, adventitia, and perivascular adipose tissue were evidenced post laser PADN. Among the identified lesions, 40% reached adventitia and could be classified as effective for PADN. The use of 20 W ablation energy was safer and 30 W-ablation led to collateral organ damage. Conclusions: An ovine model is suitable for PADN procedures; however, nerve distribution in the PA bifurcation and main branches differ from human PA innervation. Laser ablation can be safely used for PADN procedures.     

An impedance model for blood flow in the human arterial system. Part I: Model development and MATLAB implementation

An impedance model capable of predicting the time-dependent blood pressure and flow profiles in all of the vessels in the human arterial network has been developed. The model is based on a Womersley-type one-dimensional in space approximation of the pulsatile flow of a viscous fluid within elastic vessels. Nominal values from the literature are used to provide the input aortic pressure wave, the geometric dimensions of large arteries, various blood properties, vessel elasticity, etc. The necessary information to characterize the smaller arteries, arterioles and capillaries is taken from a physical scaling model [West, G. (1999). The origin of scaling laws in biology. Physica Acta, 263, 104-113]. The parameters, input setup, and the subsequent solution to the model equations have been efficiently implemented within MATLAB, which also allows for a variety of output information displays. The MATLAB implementation also allows for a comprehensive sensitivity analysis of the results to various input parameter values to be effortlessly obtained.