Adsorption Kinetics of Pb^(2+) and Cu^(2+) on Variable Charge Soils and Minerals: Ⅱ. Equations for Describing Experimental Data

Different mathematical methods, including linearization, differential, integration and nonlinear least squares approximation (Newton-Marquardt method), were used to fit different kinetic equations, such as zero-order, first-order (i. e, membrane diffusion), second-order, parabolic-diffusion, Elovich, two-constant equations, to the experimental data of Pb2+ and Cu2+ adsorption on variable charge soils and kaolinite. Assuming each M2+ occupied two adsorption sites, two more equations, the so-called surface second-order equation and third-order equation were derived and compared with the above equations according to the fitting results, which showed that the second-order equation and surface second-order equation, being one equation in different expressions under some conditions, were better than the other equations in describing the Pb2+ and Cu2+ adsorption kinetics, and the latter was the best.

A Modified Peng-Robinson Equation State for Prediction of Gas Adsorption Isotherm

This research proposes a modified two-dimensional Peng-Robinson equation model to predict adsorption isotherm in adsorbate-adsorbent systems. The parameters of the proposed model are calculated by using the optimization of experimental data for the different single gas adsorption systems at various temperatures. The experimental adsorption equilibrium data of adsorbate-adsorbent systems was compared with the calculated results in our proposed model and the two-dimensional Hill-deBoer equation model. The proposed model as indicated in the results shows a better prediction of the experimental results compared with two others.

Simulation of gas-solid adsorption process considering particle-size distribution

The particle-size distribution of adsorbents usually plays an important role on the adsorption performance. In this study, population balance equation(PBE) is utilized in the simulation of an adsorption process to model the time-dependent adsorption amount distribution on adsorbent particles of a certain size distribution. Different adsorption kinetics model can be used to build the adsorption rate function in PBE according to specific adsorption processes. Two adsorption processes, including formaldehyde on activated carbon and CO_(2)/N_(2)/CH_(4) mixture on 4A zeolite are simulated as case studies, and the effect of particle-size distribution of adsorbent is analyzed. The simulation results proved that the influence of particle-size distribution is significant. The proposed model can help consider the influence of particlesize distribution of adsorbents on adsorption processes to improve the prediction accuracy of the performance of adsorbents.

Review of Kelvin's Equation and Its Modification in Characterization of Mesoporous Materials

Physical and mathematical models as well as calculation methods of nitrogen bed on porous media have been introduced to evaluate the structural parameters of mesoporous materials. Kelvin＇s equation is a link between the relative adsorbate pressure, the mean pore radius, and pore capillarity on the basis of macroscopic capillary condensation. However, Kelvin＇s equation has been identified that it underestimates the calculated pore size of a material especially in the boundary of pore size which is between 2 and 4 nm.Various modifications on Kelvin＇s equation were mentioned in order to develop a new model to improve the accuracy of pore size calculation. The problems on conventional mathematical models were analyzed and discussed. A number of calculation methods on physisorption and pore size, especially fundamental theories of physisorption, basis of models and their deficiencies are reviewed. It can provide guidance on developing a modified Kelvin＇s equation for pore size calculation.

Adsorption Kinetics of NH_4^+ by Purple Soils with Different pH Values

Ammonium adsorption and desorption properties by purple soils with dif- ferent pH were studied. The results showed that the adsorption and desorption amounts of NH4＋ by purple soils increased with the increase of NH4＋ concentration, regardless of soil pH values; the largest adsorption and desorption amounts of NH4＋ by purple soil at pH 6.0 were 10.3 and 7.96 mg/g, respectively; the largest adsorp- tion and desorption amounts of NH4＋ by purple soil at pH 7.2 were 12.8 and 4.62 mg/g, respectively; the largest adsorption and desorption amounts of NH4＋ by purple soil at pH 8.0 were 13.5 and 2.23 mg/g, respectively. The isothermal adsorption ki- netics of NH4＋ by purple soils fits the Freundlich equation best （R〉0.95）. This study shows that the adsorption of NH4＋ by purple soils with different pH values is multi- molecular layer uneven surface adsorption.

Atrazine Adsorption Behavior on a Fluvo-Aquic Soil as Influenced by Contact Periods

A batch experiment was performed to investigate nonequilibrium adsorption behavior of atrazine （2-chloro-4-ethylamino-6-isopropylamlno-1,3,5-triazlne） on a fluvo-aquic soil. The amount of atrazine sorbed increased with increasing adsorption contact periods. For a range of initial atrazlne concentrations, the percentage of atrazine sorbed within 24 h ranged from 24% to 77% of the observed total amount sorbed for the longest contact period; when adsorption contact periods were more than 72 h, the deviations in curves fitted using a nonlinear Freundllch equation gradually became less. The opposite trend was observed for the atrazine concentrations in solution. The effect of adsorption contact periods on atrazine adsorption behavior was evaluated by interpreting the temporal variations in linear and nonlinear Freundlich equation parameters obtained from the phase-distribution relationships. As the adsorption contact period increased, the nonlinear Freundlich capacity coefficient kf showed a significant linear increase （r^2 = 0.9063, P 〈 0.001）. However, a significant negative linear correlation was observed for the nonlinear coefficient n, a dimensionless parameter （r^2 = 0.5666, P 〈 0.05）. Furthermore, the linear distribution coefficient kd ranged from 0.38 to 1.44 and exhibited a significant linear correlation to the adsorption contact period （r^2 = 0.72, P 〈 0.01）. The parameters kf and n obtained from a time-dependent isotherm rather than the distribution coefficient kd estimated using the linear Freundlich equation were more appropriate to predict the herbicide residue in the field and thus more meaningful for environmental assessment.

An improved theoretical procedure for the pore-size analysis of activated carbon by gas adsorption

Amorphous carbon materials play a vital role in adsorbed natural gas(ANG) storage. One of the key issues in the more prevalent use of ANG is the limited adsorption capacity, which is primarily determined by the porosity and surface characteristics of porous materials. To identify suitable adsorbents, we need a reliable computational tool for pore characterization and, subsequently, quantitative prediction of the adsorption behavior. Within the framework of adsorption integral equation(AIE), the pore-size distribution(PSD) is sensitive to the adopted theoretical models and numerical algorithms through isotherm fitting. In recent years, the classical density functional theory(DFT) has emerged as a common choice to describe adsorption isotherms for AIE kernel construction. However,rarely considered is the accuracy of the mean-field approximation(MFA) commonly used in commercial software. In this work, we calibrate four versions of DFT methods with grand canonical Monte Carlo(GCMC) molecular simulation for the adsorption of CH_4 and CO_2 gas in slit pores at 298 K with the pore width varying from 0.65 to 5.00 nm and pressure from 0.2 to 2.0 MPa. It is found that a weighted-density approximation proposed by Yu(WDA-Yu) is more accurate than MFA and other non-local DFT methods. In combination with the trapezoid discretization of AIE, the WDA-Yu method provides a faithful representation of experimental data, with the accuracy and stability improved by 90.0% and 91.2%, respectively, in comparison with the corresponding results from MFA for fitting CO_2 isotherms. In particular, those distributions in the feature pore width range(FPWR)are proved more representative for the pore-size analysis. The new theoretical procedure for pore characterization has also been tested with the methane adsorption capacity in seven activated carbon samples.

Prediction on adsorption ratio of carbon dioxide to methane on coals with multiple linear regression

The multiple linear regression equations for adsorption ratio of CO2/CH4 and its coal quality indexes were built with SPSS software on basis of existing coal quality data and its adsorption amount of CO2 and OH4. The regression equations built were tested with data collected from some s, and the influences of coal quality indexes on adsorption ratio of CO2/CH4 were studied with investigation of regression equations. The study results show that the regression equation for adsorption ratio of CO2/CH4 and volatile matter, ash and moisture in coal can be obtained with multiple linear regression analysis, that the influence of same coal quality index with the degree of metamorphosis or influence of coal quality indexes for same coal rank on adsorption ratio is not consistent.

Ion Exchange Adsorption Kinetics of Miglitol by D001 Resins

In order to explore internal factors for adsorption kinetic effect of miglitol by D001 resin, a batch adsorption operation for miglitol kinetic adsorption at different concentrations, temperatures and vibrating rates was investigated in oscillator (SHZ-A), respectively. The different kinetic mathematical model, Webber-Morris kinetic equation, film diffusion coefficient equation and kinetic boundary model were all applied to discuss the adsorption process. The results showed that Type 1 pseudo-second order kinetic equation can be all used to describe miglitol adsorbed by D001 resin at different concentrations, temperatures and vibrating rates. Moreover, the total activation energy (Ea) can be calculated and its value is 9.7 kJ/mol, and then calculated values of the process film diffusion coefficient and pore diffusion coefficient, it may be inferred from these gotten values that the ion exchange process is all mainly controlled by film diffusion. Therefore, the results also suggest that the external adsorption factors such as solute concentration, temperature and vibrating rate for effect of mass transfer diffusion process control of miglitol onto D001 resin are relatively weak.

Cluster Growth Through Monomer Adsorption Processes

We propose a monomer adsorption model, in which only the monomers are allowed to diffuse and adsorb onto other clusters. By means of the generalized rate equation we investigate the kinetic behavior of the system with a special rate kernel. For the system without monomer input, the concentration aj（t） of the Aj clusters （j 〉 1） asymptotically retains a nonzero quantity, while for the system with monomer input, it decays with time and vanishes finally. We also investigate the kinetics of an interesting model with fixed-rate monomer adsorption. For the ease without monomer source, the evolution of the system will halt at a finite time; while the system evolves infinitely in time in the case with monomer source. Finally, we also suggest a connection between the fixed-rate monomer adsorption systems and growing networks.

Study on the Irreversible Thermodynamics of a Marine Engine Exhaust-powered Adsorption Refrigerating System

This study investigates the heat and mass transfer mechanism of a marine engifie exhaust-powered adsorption refrigerating system by using irreversible thermodynamics. The equations of entropy-production rate and the linear phenomenological equations of thermodynamic flux and force are established. The conventional experimental facilities of unit tube are developed and the phenomenological coefficients are obtained by fitting the experimental data. It is concluded that the thermodynamic process in the adsorbent bed is determined by the coupling effect of the heat and mass transfer; furthermore, the mass transfer is determined by the heat transfer. Taking some measures to increase heat transfer can improve the performance of the adsorption refrigerating system. The conclusions presented in this paper may be of value to the engineering applications of the system.

Correlation between coal characteristics and methane adsorption on China＇s coals

It is highly important to investigate relationship between coal characteristics and methane adsorption on coal in the fields of coalbed methane recovery. Based on data examination of coal quality indexes collected from the literatures, regression equations for Langmuir adsorption constants, VL or VLIPL, and coal quality indexes for selected coal samples were developed with multiple linear regression of SPSS software according to the degree of coal metamorphosis. The regression equations built were tested with data collected from some literatures, and the influences of coal quality indexes on CH4 adsorption on coals were studied with investigation of regression equations, and the reasons of low accuracy to Langmuir constants calculated with regression equation for a few coal samples were investigated. The results show that the regression equations can be employed to predict Langmuir constants for methane adsorption isotherms on coals obtained using volumetric gas adsorption experiments, which are conducted at 30 ℃ on a wet or dried coal samples with less than 30% ash content in coal. The influence of same coal quality index with various coal rank or influence of various coal quality indexes for same coal rank on CH4 adsorption is not consistent. The regression equations have different accuracy to different coal rank, in which the VL equations supply better prediction accuracy for anthracite and higher prediction error for lower metamorphosis coal, and the PL prediction error with VL and VL/PL equations is lower to bituminous coal and higher to anthracite.

Analogy between adsorption and sorption： An elementary mechanistic approach. I. Monolayer adsorption and sorption without solvent cluster formation

The elementary mechanistic model of adsorption and sorption is based on a simple hypothesis： the adsorption sites are uniformly distnbuted on the surface of the pore walls in the adsorbent, the sorption sites are uniformly distributed in the volume of the polymer. In this first paper we will analyze the simple case where one solute molecule is only allowed to occupy a single adsorption or sorption site. A common elementary occupation law of the free sites is assumed： the differential increase of the number of the adsorbed/sorbed molecules is proportional to the differential increase of the activity of the solute and the concentration of the free （non-occupied） sites in the solid. The proportionality coefficient is called affinity coefficient depending on the solid/solute couple and on the temperature and independent of the concentration of the solute. In adsorption the concentration of the free sites is a surface concentration on the pore walls and in sorption it is expressed by the molarity. The simple monolayer adsorption law of Jovanovic is obtained： n = no（1 - e KP） where n is the number of moles adsorbed when the pressure is P. no is the total number of adsorption sites and K the affinity coefficient for adsorption. The sorption law writes： a = 1/k [Ф/1-Ф] ＋ 1-r/k In [1 ＋ 1/r Ф/1-Ф] where Ф, r and k hold respectively for the volume fraction of the solvent in the polymer, for the ratio of the molar volumes of the solvent to the elementary polymer chain containing one single adsorption site and for the sorption affinity coefficient. The confrontation of these equations to experimental isotherms is satisfactory in comparison with the classical Langmuir and Flory-Huggins equations： the best results are obtained for adsorption of vapors on a 5A zeolite and for all analyzed sorption results.

计算机模拟在物理化学BET多分子层吸附理论教学中的应用

BET多分子层吸附理论抽象但应用广泛,BET公式的推导过程涉及较多数学知识,学生很难透彻理解BET公式的物理意义。面对比表面分析仪输出的吸附脱附等温线和比表面积,学生只能生搬硬套,难以达到预期的教学效果。本文利用计算机模拟气体分子在固体表面的吸附脱附过程,通过调整吸附脱附常数,可分别得到第I、II、III类吸附等温线;结合实时可视化使学生能直观看到气体分子在固体表面的吸附脱附动力学,从而能更好地理解BET理论。计算机模拟辅助教学还能活跃课堂气氛,实现教与学互动,激发学生的求知欲和科研兴趣,提高教学质量。

固态胺吸附去除CO_(2)行为研究

为解决基于固态胺材料的再生式CO_(2)去除技术在便携式生保系统中的应用问题,开展了固态胺材料吸附去除CO_(2)的性能研究。进行了不同吸附温度、入口CO_(2)浓度、气体流量条件下固态胺吸附CO_(2)的穿透试验,获得了相应的穿透曲线;利用Wheeler方程对穿透曲线进行了拟合,得到了相应的拟合方程、平衡吸附量等结果。结果表明:通过Wheeler方程能够准确描述固态胺吸附CO_(2)的行为;获得了CO_(2)穿透率分别为10%和50%时的穿透时间与气体流量间的线性关系方程,方程可应用于预测固态胺反应器性能、切换周期等,使评估反应器性能的试验大为简化。

浮选固液系统的热力学理论及应用

浮选是发生在固液界面的物理化学行为,涉及多种物质组分之间的相互作用,是浮选理论研究的难题之一。同时,多种浮选药剂联合使用,提高矿物的浮选效果,是提高难处理矿产资源高效利用的有效手段。但对浮选固液复杂系统的研究极其困难,至今没有形成系统的理论,组合药剂提高浮选效果的物理机制也还没有获得统一的认识,这都限制了浮选理论的发展和浮选技术的进步。基于热力学基本方程,研究了浮选过程中药剂在矿物表面吸附的熵变和吉布斯自由能变化,构建了各种物质组分相互作用的热力学平衡方程组,提出了反映浮选药剂在矿物表面吸附能力的吸附平衡常数。应用浮选热力学平衡方程组,揭示浮选中各种矿物表面同质化效应的物理本质,推导出了浮选溶度积理论、双电层理论、吸附理论的数学表达式。建立了通过增加矿物表面吸附浮选药剂种类,提高浮选药剂的吸附熵变,减少吉布斯自由能变化,提高浮选药剂吸附的效率和稳定性,从而提高难处理矿物的浮选效果的高熵浮选理论和技术方法。

粉煤灰提铝残渣制备4A分子筛及Cu(Ⅱ)吸附研究

4A分子筛由于其优异的阳离子交换能力,成为处理重金属废水优良的吸附材料。为了达到以废治废的目的,以粉煤灰酸法提铝残渣为原料制备地质聚合物,再经水热原位转化合成体型化4A分子筛。采用XRD、FT-IR、SEM、BET、TGA等手段对4A沸石进行表征,探讨吸附时间、Cu(Ⅱ)初始浓度、吸附剂用量及溶液p H对其吸附性能的影响,并结合动力学方程和吸附等温线模型对其吸附过程进行研究。结果表明,所合成的4A分子筛孔隙发达且微孔含量较多,总比表面积为71.85 m^(2)/g,其中微孔比表面积为53.91 m^(2)/g,微孔孔径主要集中在1.3 nm左右。体型化4A分子筛吸附Cu(Ⅱ)的最佳条件为吸附时间为240 min、Cu(Ⅱ)初始质量浓度为100 mg/L、吸附剂用量为2.0 g/L、溶液p H为6~9,此时吸附量为32.97 mg/g,Cu(Ⅱ)的去除率可达65.93%。吸附过程符合准二级动力学模型,以化学吸附为主。Langmuir模型拟合效果较好,表明Cu(Ⅱ)在合成4A沸石上的吸附过程为单分子层吸附,且拟合得到的Cu(Ⅱ)的最大吸附量为37.05 mg/g。

煤吸附CO_(2)压缩因子快速计算模型研究

为研究Virial、V-d-W、R-K、S-R-K、P-R、童景山等6种工程常用气体状态方程中适合煤吸附CO_(2)压缩因子最优方程及快速计算模型,以3种不同变质程度煤样为研究对象,采用容量法实测了试验温度为30℃时应用以上6种方程所得煤的CO_(2)吸附量、CO_(2)吸附常数及吸附等温线。研究表明:与美国国家标准技术研究所(NIST)提供的CO_(2)压缩因子相比,采用Virial状态方程得到的CO_(2)压缩因子最大、绝对误差最小,为0.38%;吸附等温线拟合优度最高,CO_(2)吸附常数a值绝对值误差最小,确定出煤吸附CO_(2)压缩因子最优方程为Virial方程;同时,提出试验温度为30℃时,CO_(2)压缩因子一种简便快捷计算模型,经检验,该模型相对美国标准计算所得CO_(2)吸附常数a值绝对值误差最大不超过1%,且操作简便,快速精确。

污染方式对典型成层土中苯胺迁移转化的影响

苯胺污染场地的治理因其特有的相间转换性质而具有挑战,污染方式对污染物的迁移转化起到关键作用,掌握苯胺在土壤环境中的迁移转化规律,预测不同污染方式对苯胺在上部低渗透、下部高渗透(low permeability zone-high permeability zone,LPZ-HPZ)的典型成层土中迁移转化的风险,对污染场地苯胺的修复方案制定具有指导意义。以贺兰山冲积扇的典型成层土为研究对象,在场地调查的基础上进行吸附/解吸实验和土柱淋滤实验,并根据污染场地条件建立苯胺迁移转化模型,研究土壤类型和污染方式(短期高剂量,1个月泄漏100 kg;长期低剂量,1年泄漏100 kg)对苯胺迁移转化规律的影响。结果表明:①研究区砂土和粉土介质对苯胺的吸附过程符合准二级动力学方程,吸附等温线满足Freundlich等温吸附模型。②TMVOC模型能够较好地模拟不同污染方式下典型成层土中苯胺的迁移转化过程。③相同泄漏量情况下,苯胺在长期低剂量污染方式下迁移更深,证明污染源浓度与迁移深度关系密切。④污染事件发生前期,在短期高剂量的污染方式下97.21%的苯胺以非水相液体(nonaqueous phase liquid,NAPL)相存在,长期低剂量污染方式下NAPL相的占比略低,为93.76%;泄漏后期,两种污染方式下均有99.8%以上的苯胺溶解为液相,并达到相间的动态稳定。⑤苯胺进入地下环境3年后,在长期低剂量的污染方式下率先在LPZHPZ界面发生突破行为,进入高渗透层后苯胺纵向迁移速度增加,对地层更深处造成污染,并且此时相间重分配现象最明显。因此在泄漏发生后应在苯胺进入高渗透介质前及时补救,最晚不应超过泄漏事件发生后3年,且前期修复方案选择着重苯胺的NAPL相修复,后期选择利于液相苯胺修复的方案。

考虑吸附历史的污染物迁移过程及滞后特征研究

为了更好探究污染物在土壤中的迁移规律,明确土壤的吸附-解吸附机理,在非线性非均衡模型的基础上考虑多孔介质非原始吸附时吸附能力的衰减,建立考虑吸附历史效应的吸附-解吸模型进行研究。首先对该模型中初始吸附过程衰减参数、解吸过程衰减参数以及解吸比的影响效应进行分析,再对比分析吸附历史模型、非线性非均衡模型和线性非均衡模型的数值计算结果。结果表明:吸附历史模型的峰值浓度在各个位置处都为最高,其次是非线性非均衡模型,浓度峰值最低的是线性非均衡模型。吸附历史模型的吸附能力最弱,非线性非均衡模型次之,线性非均衡模型吸附能力最强;随着距离与时间的增加,三种模型的浓度差距会越来越大,而吸附历史模型的浓度峰值时刻出现最早,非线性非均衡模型次之,峰值时刻出现最晚的是线性非均衡模型。利用悬浮颗粒穿透土柱试验结果与数值模拟结果进行对比分析,结果吻合较好,说明所提出的模型能更好地反应实际污染物的迁移情况。