Isotherms for the sorption of zinc and copper onto kaolinite: comparison of various error functions

In this research, the equilibrium sorption of Zn(II) and Cu(II) by kaolinite was explained using the Freundlich, Langmuir and Redlich–Peterson isotherms, via both linear and non-linear regression analyses. In the case of non-linear regression method, the best-fitting model was evaluated using six different error functions, namely coefficient of determination (r ²), hybrid fractional error function (HYBRID), Marquardt’s percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (SSE) and sum of the absolute errors (EABS). The examination of error estimation methods showed that the Langmuir model provides the best fit for the experimental equilibrium data for both linear and non-linear regression analyses. The SSE function was found to be a better option to minimize the error distribution between the experimental equilibrium data and predicted two-parameter isotherms. In the case of three-parameter isotherm, HYBRID was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. Non-linear method was found to be more appropriate method for estimating the isotherm parameters.     

Adsorption isotherm models and error analysis for single and binary adsorption of Cd(II) and Zn(II) using leonardite as adsorbent

Leonardite, a by-product from coal mines, was applied to adsorb Cd(II) and Zn(II) from aqueous solutions. Individual and simultaneous adsorptions of the two metal ions were investigated. In a single-component adsorption system, Langmuir and Freundlich isotherms were fitted to the adsorption data. Linear and nonlinear regression methods were used for the assessment of the optimum adsorption isotherm. Error functions including root-mean-square error, sum of the squares of the errors, mean absolute percentage error, Marquardt’s percent standard deviation (MPSD), and Chi-square were applied in the nonlinear regression. The most suitable model for the adsorption of Cd(II) and Zn(II) in the single system is the Freundlich isotherm. The isotherm parameters calculated by MPSD provided the lowest sum of normalized error (SNE) value. The adsorption capacity was found to be 23.89 mg/g for Cd(II) and 16.86 mg/g for Zn(II). It was observed that the adsorption of Cd(II) on leonardite is greater than that of Zn(II). For binary component adsorption systems, Cd(II) and Zn(II) showed antagonistic behavior. The presence of the other metal ions could decrease the amount of metal adsorbed. Binary adsorption of Cd(II) and Zn(II) was tested with regard to four multi-component isotherms: Extended Langmuir, Modified Langmuir, Sheindorf–Rebuhn–Sheintuch, and Extended Freundlich. The Extended Freundlich isotherm proved to be a good fit for the experimental data.     

Multiscale estimation of the Freundlich adsorption isotherm

Adsorption plays an important role in water and wastewater treatment. The analysis and design of processes that involve adsorption rely on the availability of isotherms that describe these adsorption processes. Adsorption isotherms are usually estimated empirically from measurements of the adsorption process variables. Unfortunately, these measurements are usually contaminated with errors that degrade the accuracy of estimated isotherms. Therefore, these errors need to be filtered for improved isotherm estimation accuracy. Multiscale wavelet based filtering has been shown to be a powerful filtering tool. In this work, multiscale filtering is utilized to improve the estimation accuracy of the Freundlich adsorption isotherm in the presence of measurement noise in the data by developing a multiscale algorithm for the estimation of Freundlich isotherm parameters. The idea behind the algorithm is to use multiscale filtering to filter the data at different scales, use the filtered data from all scales to construct multiple isotherms and then select among all scales the isotherm that best represents the data based on a cross validation mean squares error criterion. The developed multiscale isotherm estimation algorithm is shown to outperform the conventional time-domain estimation method through a simulated example.     

Using Bayesian Statistics to Capture the Effects of Modelling Errors in Inverse Problems

When the parameters of a numerical model are adjusted, so that the predictions of the model match measurements from the real system, we need to take account of two sources of errors. These being measurement errors and modelling errors. Measurement errors are commonly considered, and a number of different approaches are in general usage, the most common being the weighted sum of squares method. In this paper the standard Bayesian equation, used for inverse problems, is reformulated so as to make it more intuitive to use. This allows the inclusion of both a modelling error and correlations between measurements to be carried out easily. The results are tested on a simple one-parameter numerical model and a cross-sectional model of a petroleum reservoir. In the first case the proposed error model appears to work well. In the second case it appears that the objective function is multimodal, leading to multiple acceptable solutions. The results of this paper are important to those whose numerical models are thought to contain significant modelling error. This encompasses many areas of modelling related to earth science and engineering.     

Sublethal Effects of Crude Oil on the Community Structure of Estuarine Phytoplankton

While the ecological impacts of crude oil exposure have been widely studied, its sublethal effects on phytoplankton community structure in salt marsh estuaries have not been well documented. The purpose of this study was to simulate oil spill conditions using a microcosm design to examine short-term (2 day) changes in phytoplankton community composition and total biomass following exposure to crude oil obtained from the Deepwater Horizon oil spill and a mixture of Texas crude oils. Microcosm experiments were performed in situ in North Inlet Estuary near Georgetown, SC. A control and six replicated experimental treatments of crude oil additions at final concentrations of 10, 50, or 100 μl l⁻¹ of either Deepwater Horizon spill oil or the Texas crude mixture were incubated under in situ conditions. Photopigments were analyzed using high-performance liquid chromatography and community composition was determined using ChemTax. Total phytoplankton biomass (as chl a) declined with increasing crude oil concentrations. Prasinophytes, the most abundant microalga in both experiments, showed no response to oil exposure in one experiment and a significant negative response in the other. Diatoms euglenophytes and chlorophytes appeared relatively resistant to oil contamination at the exposure levels used in this study, maintaining or increasing their relative abundance with increasing oil concentrations. Chlorophytes and cyanobacteria increased in relative abundance while cryptophyte abundance decreased with increasing oil concentrations. The results of these experiments suggest that low levels of crude oil exposure may reduce total biomass and alter phytoplankton community composition with possible cascade effects at higher trophic levels in salt marsh estuaries.     

Retention of a heavy metal by marl collected from aquifer substratum

One of the objectives of this work is to characterize marl samples collected from the bedrock aquifer (at 30 m depth) of Wadi Al Ghoula located in Draria southwest of Algiers. The other objective is to make a kinetics study, linear and non-linear isotherm study, and mass transfer study of the adsorption of copper onto marl in aqueous solution. The fitness of kinetics and isotherm models was evaluated by using some error analysis function. One of the major results using an XRF technique is an evidence of the presence of calcite in the weight of 13.82%. The XRD patterns of these samples confirmed the presence of montmorillonite, kaolinite, illite, calcite, and quartz. On the other hand, the FTIR analysis clarified the presence of calcite. The specific surface area of 20,999 m²/g was obtained using the BET, which indicates that the material has a predominance for the mesoporous character. The instrumental neutron activation analysis (INAA), a nondestructive method, gives the elemental composition of the adsorbent. Based on the value of the coefficient of determination, the adsorption kinetics of copper in aqueous solution using marl as adsorbent follows the pseudo-second-order model. And according to the value of the coefficient of determination obtained for the two models, the intraparticle diffusion and liquid film diffusion control the process of adsorption of copper onto marl with low predominance for the second model of diffusion in the first stage of adsorption. The linear and the non-linear treatments of the two-parameter isotherm models (Langmuir, Freundlish, Temkin) show that the fitting best model of isotherm is the empirical Freundlish isotherm. For the three-parameter isotherm models (Toth, Sips, and Redlish-Peterson), the Sips model is the more accurate fitting model than the two other isotherms in the non-linear approach. Some error analysis functions are used to choose the best results.     

Real-time application of an oil spill movement prediction system

This paper deals with the prediction, in real time, of the motion of experimental oil slicks. The experiments were conducted during September 1983 offshore near Halifax on the east coast of Canada. The objectives of the experiments were (i) to determine the suitability of oil spill dispersants as countermeasures and (ii) the testing and verification of oil spill trajectory models and systems.The Atmospheric Environment Service (AES) participated in the experiments to test the capability of its oil spill motion prediction system in providing real-time trajectory forecasts. The experiment consisted of three sets of spills. Each set had a control slick and a test slick. Sixteen barrels of crude oil were used in each spill. The test slicks were used to test the effectiveness of various dispersants, the control slicks were used to verify trajectory forecasts.The spill trajectories and oil weathering information obtained from the system during the experiments demonstrated the relative ease with which the system could handle the required input and provide timely forecasts. The accuracy of these forecast trajectories was confirmed by observations, and their utility was demonstrated by their application in the operational decision-making process.     

基于复杂地质体的地应力场智能识别方法研究

初始地应力是地下开采及施工所需要考虑的重要影响因素,地应力值的准确获得通常采用现场测量与反演计算结合实现。针对某铜镍矿复杂地质体,在已有监测数据的基础上建立三维正交数值模型,获得监测点的地应力计算值。利用遗传规划程序,回归地应力监测点的地应力与各自变量的函数关系。建立地应力实测值和计算值之差的平方和最小的目标优化函数,使用遗传算法智能算法对目标函数进行优化,最终获得了矿区的原岩应力场。检测样本验证结果显示,计算值与实测值的误差控制在10%以内,一定程度上证明了该地应力场智能识别方法的可靠性,可为以后复杂地质体矿区地应力场的计算提供较为可行的研究方法。     

Nitrate sorption by organosmectites

The use of organoclays as adsorbents in the remediation of polluted water has been the subject of many recent studies. In this present work, a Tunisian smectite modified by two cationic surfactants was used as a sorbent for the investigation of the adsorption kinetics, isotherms and thermodynamic parameters of nitrate ions at various contact time, initial concentrations and temperatures. Two simplified kinetic models, first-order and second-order, were used to predict the adsorption constants. It was found that the adsorption kinetics of nitrate was best described by the second-order model. Adsorption isotherms and equilibrium adsorption capacities were determined by the fittings of the experimental data to two well-known isotherm models including Langmuir and Freundlich. The results showed that Langmuir model appears to fit the adsorption better than Freundlich model. The equilibrium constants were used to calculate thermodynamic parameters, such as the change of free energy, enthalpy and entropy.     

An analysis of history matching errors

We use a simple 2D model of a layered reservoir with three unknown parameters: the throw of a fault, and high and low permeabilities. Then consider three different cases where in each case two parameters are kept fixed and the third one is varied within a specific range. Using a weighted sum of squares of the difference in production for the objective function, we plot it against the varying parameter for each case. It mainly shows a complex function with multiple minima. We see that geological ‘symmetry’ and also vertical spreading are some sources of non-monotonicity in the production and transmissibility curves. These result in a multi-modal objective function and consequently non-unique history matches. The behaviour of the system in the forecast period is also studied, which shows that a good history matched model could give a bad forecast.     

Adsorption of oxyanions by spent western oil shale: II. selenite

The adsorption and desorption behavior of selenite by processed Green River Formation oil shales were examined. The selenite adsorption data could be quantitatively described by both the Freundlich and Langmuir isotherms. However, greaterR ² values were obtained for the Freundlich isotherms. Furthermore, selenite adsorption was not a function of the extraction process. The adsorption of selenite by the processed oil shales was irreversible. Upon dilution of the equilibrium systems, additional selenite removal from solution occurred. A thermochemical analysis of the adsorption and desorption equilibrium solutions indicated that the solutions were undersaturated with respect to a number of metal selenite solids. This indicates that precipitation processes are not influencing selenite behavior. However, not all selenite minerals were examined in the evaluation because of the lack of thermochemical data. An insufficient equilibration period for the adsorption study or the alteration of processed oil shale solids as a result of hydration reactions may also have hastened the additional removal of selenite during the desorption studies.     

Gravity field recovery from airborne gradiometer data using collaction and taking into account correlated errors

Least squares collocation is a very comprehensive method for gravity field modelling, since it may use known noise characteristics of the data. In many earlier applications the errors affecting the data were considered uncorrelated, mainly due to the difficulty in estimating the systematic character of such kind of errors. In this study, error covariance functions of airborne gravity gradiometer data are estimated by comparing model covariance functions with empirical covariance functions of the gravity gradiometer data. The model covariance functions were estimated from accurate surface gravity data and continuated upward to the height of the airborne measurements using the covariance propagation law. The estimated error covariance functions were modeled as finite ones and used as an additional information for the prediction of gravity anomalies from gravity gradiometer data. The assessment of the prediction results was made by comparing the gravity values predicted from the airborne gradient data and showed up to 25% improvement compared to not using correlated errors.     

Causes and consequences of errors in determining sorption capacity of coals for carbon dioxide at high pressure

Recent comparisons of CO₂ sorption by coals at high pressures have shown major differences between the results obtained by different laboratories. These need to be resolved for laboratory estimation of CO₂ sequestration in coal seams to be useful. A compilation of potential sources of error in determination of sorption characteristics and their impact on sorption measurements is provided here. A series of tests is also provided that can be used to identify and reduce such errors in measurement. For example, an error in temperature produces a characteristic distortion of the sorption curve for carbon dioxide, which can be corrected to some extent. A negative value for excess sorption at high pressure is almost certainly diagnostic of either a cell volume that has been overestimated or that some part of the substrate that is inaccessible to the gas is accessible to helium. The major source of variation between results from the different laboratories that supplied the closest sorption values was found to be variations in the assumed free space volume, which could be due to discrepancies in determined helium density or measured cell volume. Including a term in the sorption model that is proportional to gas density will markedly reduce the influence of such errors in estimating sorption capacity or heats of sorption. The influence of swelling and moisture on sorption isotherms is also quantified here. Correction for swelling of coals in carbon dioxide changes the estimated sorption capacity by less than 1%, if a term that is proportional to gas density is included as a free parameter in the model fitting the isotherm.     

Scaled total-least-squares-based registration for optical remote sensing imagery

In optical image registration, the reference control points (RCPs) used as explanatory variables in the polynomial regression model are generally assumed to be error free. However, this most frequently used assumption is often invalid in practice because RCPs always contain errors. In this situation, the extensively applied estimator, the ordinary least squares (LS) estimator, is biased and incapable of handling the errors in RCPs. Therefore, it is necessary to develop new feasible methods to address such a problem. This paper discusses the scaled total least squares (STLS) estimator, which is a generalization of the LS estimator in optical remote sensing image registration. The basic principle and the computational method of the STLS estimator and the relationship among the LS, total least squares (TLS) and STLS estimators are presented. Simulation experiments and real remotely sensed image experiments are carried out to compare LS and STLS approaches and systematically analyze the effect of the number and accuracy of RCPs on the performances in registration. The results show that the STLS estimator is more effective in estimating the model parameters than the LS estimator. Using this estimator based on the error-in-variables model, more accurate registration results can be obtained. Furthermore, the STLS estimator has superior overall performance in the estimation and correction of measurement errors in RCPs, which is beneficial to the study of error propagation in remote sensing data. The larger the RCP number and error, the more obvious are these advantages of the presented estimator.     

Adsorption capacity and mineralogical and physico-chemical characteristics of Shuwaymiyah palygorskite (Oman)

In this paper, Shuwaymiyah palygorskite in the Sultanate of Oman has been characterized mineralogically by X-ray diffraction (XRD) and electron microscopy, chemically by oxide compositions, structural formulae, and cation exchange capacity (CEC), and physically by specific surface area and adsorption isotherms. Batch adsorption studies were performed to evaluate the adsorption performance of methylene blue (MB) basic dye on the local clay mineral. The quantitative XRD analysis indicates that the purity of some selected samples of palygorskite clay is very high (about 70% of the clay minerals are palygorskite and 30% kaolinite). The scanning electron microscopy (SEM) and transmission electron microscopy (TEM) images clearly support this conclusion. The adsorption equilibrium revealed that Shuwaymiyah palygorskite clay can uptake up to 51 mg of MB per 1 g mass of clay. MB adsorption is best fitted by Langmuir isotherm, and a pseudo-second-order kinetic model can be efficiently used to predict the kinetic of adsorption of MB by the palygorskite. The results obtained from these laboratory-scale adsorption tests indicate the promising adsorption capability of the Omani palygorskite.     

回归模型的灵敏度分析

回归计算中，由于资料和计算上的误差，使结果也产生一定的误差，通常，采用最小二乘法或最小一乘法来估计回归模型中的参数，即是取目标函数为最小来实现的，如果使目标函数在允许的误差范围内变化，则参数会有相应的变幅，本文探讨了两变数回归时参数估计的灵敏度，在相关关系不甚密切时，误差对结果的影响是较大的。     

拉格朗日乘子法在水位流量关系拟合中的应用

针对传统方法在水位流量关系拟合中线性化后存在的不足以及未考虑拟合函数的显著性水平的局限性,以流量残差平方和最小为目标函数,以显著性水平为约束条件,结合拉格朗日乘子法对水位流量关系进行优化处理。通过算例对比分析了水位流量关系在传统算法、自适应加速遗传算法及本文优化算法下的拟合结果。计算结果表明:提出的优化理论能更精确地模拟实际工程中水位流量关系,其基本思想可为类似的水文分析提供借鉴作用。     

Tracing subsurface oil pollution leakage using 2D electrical resistivity tomography

This study provides an evaluation of the subsurface oil contaminant flow in an oil production field at the Wadi Feiran fan, along the Gulf of Suez, Egypt. The 2D electrical resistivity tomography technique has been applied along four profiles surrounding the spill location of oil dump site. Theoretical soil resistivity response versus fluid resistivity for different cation exchange capacity values has been studied. Then, a physical model for the current situation of flowing the oil over the groundwater (sea invaded water) of saturated fluvial sediments has been introduced. It was supposed that the crude oil has higher resistivity values and turned to be conductive far away from the oil spill source under the effect of microbial biodegradation. Such conditions of contaminated distribution and its resistivity values have been considered during the inversion and interpretation of the acquired data sets. The processed 2D resistivity profiles reveal that oil plumes are accumulated in the seawater invasion direction, whereas it has low signatures along the profiles parallel to the shore line.     

模糊模式识别法在评价地下水水质中的应用

采用模糊模式识别法评价地下水水质,提出了相对隶属度理论,通过距离平方和最小的准则,建立目标函数,可得地下水水质的变化趋势,更符合当代地下水水质评价的要求。应用该法评价太原市地下水,得到了满意的结果。     

Multimedia environmental analysis of PCBs fate and transport mechanism through a case study of transformer oil leakage

Transformer oil leakage having large quantity of PCBs is one of the most deplorable incidents resulting in huge negative impacts on the environment. In this paper, two different models, i.e. CHEMCAN and the hydrocarbon spill screening models, were applied to the case study adapted from a real case of PCBs in transformer oil spill in Montreal. The oil migration was examined in three dimensions including site-specific data, soil characteristics and hydrogeological properties. This study aims to investigate the fate, transport and transformation rates of PCB in the soil, the unsaturated and the saturated zones. The proposed modelling concept helps to define the processes to be used in characterization of soil and subsurface environment as a receptor of transformer oil spill. This study includes the simulation techniques for assessing the effect of PCBs on groundwater and soil. Results from multimedia environmental model and HSSM model verify with each other, and both show that 92.7 % of PCBs were found in soil as compared to groundwater. Considering decay and sorption processes at spill location, concentration of PCBs in soil was >50 mg/kg. This study can serve as a basis for further analysis and assist in selection of remediation technique.