用商业氧化镁从水中移除硼的平衡，动力学和热力学研究

一种bstract

In the present work, the equilibrium, thermodynamics, and kinetics of boron removal from aqueous solutions by the adsorption on commercial magnesium oxide powder were studied in a batch reactor. The adsorption efficiency of boron removal increases with temperature from 25°C to 50°C. The experimental results were fitted to the Langmuir, Freundlich, and Dubinin–Radushkevich (DR) adsorption isotherm models. The Freundlich model provided the best fitting, and the maximum monolayer adsorption capacity of MgO was 36.11 mg·g^-1。此外，试图对伪一阶动力学模型和伪二阶动力学模型进行了实验动力学数据解释。结果表明，伪二阶动力学模型提供了最合适的。这样的结果表明，由于通过应用伪第一阶动力学模型获得的两个直斜面，吸附过程似乎发生在两个阶段中，这通过将结果的调节确认为伪二阶模型来确认。计算的激活能量（）是45.5 kj·mol^-1那和T.he values calculated forδ.G°，δ.H°，和δ.S°为-4.16 kj·mol^-1，21.7 kj·mol^-1那和8.7.。3. kJ·mol^-1， 分别。这些值证实了吸附过程的自发性和吸热性质，并表明该病症在固液界面上增加。结果表明，MgO对MgO的硼吸附过程的控制步骤是物理性质。

1。介绍

来自海洋底土的石油的勘探和生产产生大量的液体流出物，也称为产水，与原油一起提取[1]。产生的水是在海洋储层中的油中发现的水，或者注入水库的水以恢复石油。生产的水流在储层生产的早期阶段低。尽管如此，在最佳利用的井中的最终几年内，它可以达到最高达80％的原油提取[2]。

所生产的水组合物可根据井的变化而变化，通常含有高盐度，有机和无机物质，溶解固体的水平超过40％，这使其对环境有毒[2那3.]。

硼是所生产的水中存在的元素，其浓度可从4毫克·L变化^-1到350 mg·l^-1[3.那4.]。AL.T.hough boron is considered a micronutrient essential to the development of microorganisms, plants, microalgae, and animals, this element can be toxic at concentration of 0.3 mg·L^-1敏感植物，2毫克·升^-1T.O.semitolerant ones, and at 4 mg·L^-1宽容。因此，这是硼必需的原因之一，环境保护机构需要从水和其他污水中除去[5.那6.]。

这maximum boron concentration recommended by the World Health Organization (WHO) for potable water was 0.5 mg·L^-1in 1998. However, this value was modified to 2.4 mg·L^-1在2011年。根据标准的立法那T.he limit allowed by the European Union, the UK, and Japan is 1.0 mg·L^-1。在巴西和秘鲁等南美国家，淡水和废水的极限为0.5毫克^-1和5毫克·卢^-1， 分别。相反，在美国，限制不受此问题的联邦法规。明尼苏达州，佛罗里达州和加利福尼亚州的州允许限制为0.6,0.63和1 mg·l^-1那respectively [7.-11.]。

因此，含有硼的产生的水需要在释放回海或用作饮用水的水源之前进行治疗。

这re are many possible treatments for the boron removal such as the electrocoagulation, process which achieved efficiencies over 98% from synthetic solutions and real produced waters with initial boron concentration between 10 and 30 mg·L^-1[12.]。O.T.her treatments are the adsorption by different types of adsorbents, including activated carbon, fly ash, clay, mesoporous silica, oxides, nanoparticles, biological material, layered double hydroxides, and natural minerals [13.-15.]。在实验室研究了一些其他方法，例如电渗析[16.]，植物修复[17.那18.]和生物电化学系统，呈现高达90％的去除效率[19.那20.]。

然而，用于从生产的水和海水中除去硼的最广泛的方法，较大规模是反渗透和离子交换[21.那22.]。

就逆转渗透而言，硼去除可以在pH = 10.5时达到98％的值，因为在该pH下，主要的硼特性是硼酸硼离子B（OH）^4-与硼酸相比，具有负电荷和更大的尺寸（H._3.博_3.）[2那22.]。In the case of ion exchange, the removal of boron occurs via its adsorption in specific resins, which are usually synthesized by means of macroporous cross-linked polystyrene resins, and functionalized by the N-methyl-D-glucamine (1-amino-1-deoxy-D-glucitol; NMDG) group achieving removal efficiencies up to 99% [23.-26.]。

离子交换过程中使用的最常见的商业树脂是曲调CRB 02，嘌呤钛矿S108和Amberlite IRA-743 [6.那27.-30.]。

通常，用树脂处理的产生的水中硼的初始浓度可在15至60mg·l之间变化。^-1。然而，在一段时间之后，这种树脂饱和，达到突破，需要再生被重用[12.那31.]。

再生步骤包括通过酸性溶液（通常是h₂所以_4.）T.hrough a saturated resin, resulting in an acid solution with high concentration of boron, usually between 350 and 700 mg·L^-1，这也必须治疗。

这volume of this effluent containing boron is relevant when it refers by example to oil waterway terminals, such as São Sebastião Waterway Terminal from Petrobras/Brazil, with a capacity of 1,585,345 m^3.[32.]。Due to their magnitude, they generate a large quantity of effluent, which is product of the elution of the resins used at wastewater treatment plants of these terminals.

由于硼浓度高，常规技术对这种流出物的处理不足。因此，在这种情况下，诸如沉淀或吸附等技术似乎是可行的替代品。

通过这些处理，硼浓度可降低至15-30 mg·l^-1这可能允许处理废水的混合production water and these could be subsequently treated by ion exchange resins or reverse osmosis. The resulting solid residue of precipitation/adsorption process can be disposed in landfills or be used as raw material in the manufacture of glass due to its high content of boron. In this context, magnesium oxide is provided as a good alternative as it is environmentally friendly, cost-effective, and nontoxic. Furthermore, it shows low solubility in water, and it is an effective sorbent for the removal of contaminants such as fluoride and toxic dyes [33.那34.]。

本作本作的目的是评估硼从含量高含量的水溶液中除去的动力学，热力学和平衡（350 mg·L.^-1）通过在氧化镁中吸附。

2.实验

2.1。材料和方法

For each experiment, a synthetic solution of 350 mg·L^-1通过溶解硼酸（h_3.博_3.）PA in distilled water. The pH of the solution was adjusted with 1 M NaOH and/or 1 M HCl solutions provided by Sigma-Aldrich.

吸附过程中使用的氧化镁由Magnesitaa SA（MgO-500）提供。

2。2。Characterization of MgO and Boron Concentration Analysis

通过双激光液体干散分散粒度分析仪，CILAS 1064L分析MgO颗粒的尺寸。通过从PerkinElmer的电感耦合等离子体分析测定水溶液中的硼浓度，Optima 4300dv。通过扫描电子显微镜（MRV）测定MgO的形态。

2.3。实验程序

这experiments were carried out in a batch reactor with 500 mL of solution. The use of borosilicate glass beaker was to prevent further contamination by dissolution of boron substances from the silicate material (beaker), mainly because the experiments were performed at alkaline pH. The solution was stirred at a speed of 150 rpm, 40 g·L^-1加入MgO，开始实验后容易调整pH。使用pH计（Bel Engineering W3B）测量溶液的pH，并用1M NaOH和/或1M HCl溶液（Sigma-Aldrich）调节。

这study of reaction kinetic was performed by collecting the sample every 5 minutes. The samples were vacuum-filtered through a cellulose nitrate membrane of 0.4 μM孔径（甘蔗）。反应240分钟后，搅拌关闭。

通过电感耦合等离子体光谱仪（Optima 4300DV，来自PerkinElmer）保持过滤的样品。

S.imultaneously, a sludge sample was dried at 70°C and adequately stored for further analysis of the surface morphology by scanning electron microscopy (MRV).

这effect of temperature was evaluated in the process of boron removal at range of 5°C to 50°C, with initial concentration of boron of 350 mg·L^-1。对于实验期间的恒温维护，使用冷却或加热系统。

2.3.1。吸附等温线

吸附等温评估的实验在批量系统中进行，MgO浓度范围为8g·l^-1到64 g·l^-1在25℃，40℃和50℃的三种不同温度下，在240分钟内反应。

硼的初始浓度为350 mg·l^-1那T.he stirring speed was 150 rpm, the pH was 10, the temperature was at 25°C, and the volume of the solution was 500 mL. After filtration, the samples were sent to boron concentration analysis.

3.结果和讨论

3.。1。Characterization of MgO

这chemical composition provided by the manufacturer is shown in Table1。

数字1和2显示在吸附过程前后MgO-500的表面形态。图中呈现的结构差异2was due to the formation of a layer of H_3.博_3.在MgO的表面和MgO的水合成Mg（OH）₂吸附过程后。

3.2。吸附等温线

吸附等温物描述水相中材料浓度与其在颗粒吸附的表面上的浓度之间的平衡。本研究采用Langmuir，Freundlich和Dubinin-Radushkevich的模型来描述平衡吸附。

3.2。1。Dubinin–Radushkevich Isotherm

DUBININ-RADUSHKEVICH（DR）等温线是一种模型，其认为是多层和异质表面的吸附。

博士model is expressed mathematically as follows: 在哪里是每mgO吸附的硼的量（mg·g^-1），是最大的吸附容量，与吸附能量有关的常数（mol²·KJ.^-2），∈是Polanyi潜力。和表达（2） 和 （3.）， 分别 [35.]: 在哪里is the gas constant (J·mol^-1K.^-1）和温度（k）。（kj·mol^-1）是吸附能量，其值的大小表明吸附是化学或物理性质。

3.2.2。Langmuir等温线

Langmuir等温线是一种模型，将单层吸附到具有有限数量的吸附位置和均匀的吸附能量的均匀表面上，并且该模型由以下等式给出[36.]:

等式（4.）可以如下方式线性化： 在哪里是溶液中硼的平衡浓度（mg·l^-1），是吸附在MgO上的硼的量（mg·g^-1），是MgO的最大单层吸附能力（mg·g^-1）， 和琅勃马尔吸附常数与能量吸附有关（L·Mg^-1）。

3.2.3。Freundlich等温线

该模型应用于异质表面的吸附过程，可逆吸附，并承认多层吸附[37.]。

Freundlich方程及其线性形式可以如下给出： 在哪里是在平衡时吸附的硼浓度（mg·g^-1），是溶液中硼的平衡浓度（mg·l^-1）， 和（l·g^-1）和N是弗氏润肤吸附等温常数，分别与吸附能力和吸附强度有关。

数字3.显示硼MgO-500在25℃，40℃和50℃下的吸附等温线。

It can be observed that the adsorption isotherm at 25°C could be classified as an H4-type isotherm according to the classification of Giles et al. [38.]。T.his type of isotherm suggests a high affinity between adsorbate-adsorbent, and the subgroup 4 suggests the formation of monolayers of adsorbate on the surface of adsorbent.

O.NT.he contrary, for the isotherms at 40°C and 50°C, it is observed that they are similar L-type isotherms according to the classification of Giles et al. [38.]。

这种类型的等温机构假设在离子B（OH）之间存在亲和力^4-和MgO，如果填充更多的吸附剂，则将空位与其他溶质分子填充更困难。这种类型的等温线通常在以下机制下表示：（1）分子被吸附在层中，（2）在吸附分子和溶剂分子之间的吸附表面上的活性位点竞争[39.-41.]。

In the present work, the Langmuir, Freundlich, and Dubinin–Radushkevich models were evaluated, which are the most widely used models to describe an adsorption process.

根据表中所示的结果2，为实验数据提供更好拟合的模型是Freundlich的等温，在25℃，40℃和50℃下，具有99％的相关性。数字4.shows the data adjusting to the Freundlich isotherm, and Table3.compares the Freundlich isotherm parameters between MgO used at present work and other adsorbents.

Freundlich等温机构提出了异质吸附表面和可逆吸附过程，其考虑了多层的形成。但是，ION B的吸附（OH）^4-可以涉及不同的机制，例如离子交换，微腐蚀，络合/螯合和静电吸引力[40.-42.]。

获得Freundlich等温机0.33,0.51和0.57的值分别在25℃，40℃和50℃的温度下。价值N那which are related to the distribution of ion B(OH)^4-与吸附剂上的活性位点相连，分别为1.392,1.476和1.481，分别为25°C，40°C和50°C（表2）。

的价值Nis a constant that indicates the strength of adsorption and is also known as a measure of linearity sinceN等于一个。在这种情况下，吸附过程是线性的;因此，吸附位点是均匀的能量，并且在吸附物和吸附剂之间不会存在任何相互作用。对于价值观N小于单位，吸附物和吸附剂之间的连接非常弱，因此，该方法不利于吸附，其吸附容量降低。

但是，对于价值观N大于单位，吸附过程有利;因此，吸附能力增加，表明在研究的实验条件下，离子的吸附是有利的[41.-43.]。如表所示3.，所有值N大于Freundlich等温线的单元，温度从25℃升高至50℃，表明硼MgO-500的吸附受到温度的青睐。

它也可以从表中注意到3.T.hat the adsorption constants (）对于不同温度下的硼去除过程高于与活性炭，活性氧化铝，丙烯（76％Al₂O._3.），Siral（28％SIO₂，72％的人₂O._3.），T.annin gel, and mineral wastes. It is clear that the capacity of boron adsorption by MgO is higher than other adsorbents with exception to N-methyl-D-glucamine onto SPC and neutralized red mud.

3.3。动力学分析

这K.inetics of boron removal by adsorption onto MgO was studied in the present work. The rate in which boron is removed by adsorption is the most important parameter for the design of a continuous or batch system in an effluent treatment plant. Therefore, it is essential to establish the dependency of time in the adsorption process for different operational conditions.

这K.inetics of adsorption depends on the adsorbate-adsorbent interaction. The rate of adsorbate removal determines the residency time required for complete adsorption and could be calculated by kinetic analysis.

3.3。1。Equilibrium Kinetics

在吸附过程中，吸附溶质倾向于解吸并返回溶液，反之亦然。该过程连续发生，直到在给定时间，吸附和解吸率达到平衡状态。因此，在该阶段，在解决方案中不会有任何额外的污染物吸附[45.-47.]。

T.ests were conducted to determine the equilibrium of the reaction under the following conditions: 500 mL solution with a concentration of 350 mg·L^-1硼准备;然后，加入MgO以获得40g·L的浓度^-1，将pH以10和搅拌速度为150rpm。在不同的时间段（5,10,15,20,25,30,40,50,60,60,140,​​190和240分钟）上收集样品。

数字5.shows the effect of temperature on boron removal.

这maximum adsorption capacities were 7.2, 7.7, and 8.0 mg·g^-1在25℃，40℃和50°C的温度下。

It can also be observed, according to Figure5.那T.hat the rate of the process is greatly affected by an increase in temperature, and at 25°C, 40°C, and 50°C, the equilibrium of reaction was reached around 40 min, 30 min, and 15 min, respectively. From this stage, the variations in adsorption capacities were insignificant. Figure5.also shows that the period of time for reaching equilibrium at temperatures of 40°C and 50°C is relatively short, which could be an advantage for future industrial applications.

3.3。2。K.inetic Models

In 1898, Lagergren presented the kinetic model known as “pseudo-first-order equation” for a liquid-solid system based on the adsorption capacity of the solid.

Later, Ho and Mckay [46.]基于溶液中的污染物的浓度来提出Laggrgren模型，称为“伪二阶方程”。

接下来，将提出基于这些模型的动力学分析，这是这种类型吸附过程的最常见和良好的。

（1）伪一阶动力学模型。Laggrgren模型是为固液吸附系统开发的，基于吸附剂的吸附容量。等式（7.）shows how this model is usually expressed, being one of the most used models to study the kinetics of adsorption processes:

数字6.和7.将实验数据在25°C，40°C和50°C下施加到伪第一阶模型。

It is observed in Figure6.动力学曲线存在明显的多线性，这可能导致我们认为该过程发生在两个阶段。数字7.shows the good fit of the experimental kinetic data at 25°C in the pseudo-first-order model withR.² = 0.96.

(2) Pseudo-Second-Order Kinetic Model。伪二阶模型基于溶液中污染物的浓度。吸附速率方程可以如下写入： 在哪里吸附速率常数（g·mg^-1·Min.^-1），是在平衡下吸附的硼的浓度（mg·g^-1）， 和是在吸附剂表面上的硼浓度(mg·g^-1）。可以通过绘制实验确定常数相对 。

数字8.图示了将实验数据调整到伪二阶动力学模型。桌子4.presents the values of the kinetic parameters obtained from this setting.

It can be observed from the values presented in Table4.伪二阶模型是具有吸附过程的实验数据的最佳拟合的伪二阶模型。R.²values of 0.99 were obtained for this model at the three temperatures studied (25°C, 40°C, and 50°C) compared to theR.²在相同温度下分别为0.96,0.83和0.43的伪第一阶模型获得的值。

价值在伪二阶模型中在25℃，40℃和50℃下获得7.81mg·g^-1那8.。12. mg·g^-1那和8.。17. mg·g^-1那respectively, while the experimental values obtained at the same temperatures were 7.23 mg·g^-1，7.75 mg·g^-1那和7.。9.8. mg·g^-1， 分别。It can be observed from the comparison of the values of通过实验获得，并通过伪二阶模型来实现值非常相似，证实通过用MgO吸附除去硼的方法遵循伪二阶动力学。

文献中的研究表明，许多模型对整体吸附过程提供了澄清。但是，在许多情况下，当图表存在多线性特征时是不可能的[48.]。

为了了解这些情况，通常将图形分成两条或更多个直线，并表明吸附机制由每个直线控制。这种做法有助于在一定程度上理解吸附机制[48.]。

从图中6.代表experime的应用NT.al data to a pseudo-first-order kinetic model, it is observed that the adsorption process at the three temperatures seems to occur in two stages due to the two straight slopes obtained from the application of the model, which is confirmed by the adjustment of the results to the pseudo-second-order model that describes a two-step reaction occurring consecutively.

3.3。3.。一种pparent Activation Energy

计算吸附过程的表观激活能量。根据温度的增加，速率常数的变化可以由Arrhenius方程描述（9.）： 在哪里吸附速率常数（g·mg^-1·Min.^-1），is the independent factor of temperature (g·mg^-1·Min.^-1），是吸附活化能量（KJ·mol^-1），是气体常数（8.314 j·mol^-1·K.^-1）， 和是溶液的温度（k）。

等式（10.）可以以线性形式表达，如下：

如图所示8.那T.here is a linear correlation between the rate constant of the pseudo-second-order model and its corresponding absolute temperature, with a correlation coefficient of 0.98. Figure9.shows the correlated experimental data in the linearized Arrhenius equation. From Figure9.，之间的关系和can be represented as follows:

从 （11.），我们可以观察到频率因子是3.02×10^6. g·mg^-1·Min.^-1，激活能量为45.54 kj·mol^-1，这在建议的正常范围内非常略微略微（8-40kJ·mol^-1）对于典型的物理吸附过程[49.-52.]。

3.4。过程的热力学

In order to understand the thermodynamics of the process of boron removal by adsorption with MgO, some thermodynamic parameters were determined. Adsorption tests at different temperatures were performed using a thermostatic bath, under the following conditions: initial boron concentration = 350 mg·L^-1，pH = 10，MgO浓度= 40 g·l^-1，搅拌速度= 150rpm。

这T.emperatures studied were 25°C, 40°C, and 50°C, and the parameters calculated were standard Gibbs free energy variation (δ.G°), standard enthalpy variation (δ.H°), and standard entropy variation (δ.S.°）。

吸附过程的标准自由能变化与平衡常数有关（）和can be calculated according to the following equation: 在哪里是气体常数（8.314 j·mol^-1·K.^-1），是绝对温度，还有is the equilibrium constant, which can be estimated from the following equation: 在哪里 is the concentration of boron at equilibrium in the solution (mg·L^-1）和 is the concentration of boron at equilibrium in the adsorbent (mg·L^-1）。

这variations in standard enthalpy (δ.H°）和标准熵（δ.S.°）可以根据以下Van't Hoff等式计算：

数字9.represents the plot of相对1/T.从Van't Hoff方程式，线的斜率是和T.he intercept withy-AXIS是 那from which the corresponding thermodynamic parameters were obtained and are presented in Table5.。

从表格5.，可以观察到，当吸附过程的温度从25℃增加至40°C和40℃至50°C时，δ.G° values become increasingly negative varying from −4.16 kJ·mol^-1到-5.88 kj·mol^-1从-5.88 kj·mol^-1T.O.-6.26 kJ·mol^-1， 分别。这意味着由于负值的所有温度都是自发的δ.G°. Likewise, as the temperature increases, the B(OH)_4.^-离子具有较高的亲和力，可以通过MgO吸附。

这δ.G° for physical sorption is between −20 and 0 kJ·mol^-1并且范围从-80到-400 kj·mol^-1用于化学吸附[52.那53.]。价值δ.G° presented in Table5.indicate that the sorption process is controlled by physical adsorption.

这adsorption enthalpy is also a parameter used to indicate the intensity of the interaction between the adsorbate and the adsorbent. In the phenomenon of physisorption, this parameter has low values (up to about 40 kJ·mol^-1）由于它的特征在于相互作用程度的特征，因此涉及范德华力量幅度的力量涉及的力。化学吸附现象的特征在于吸附剂与吸附剂表面之间的高度相互作用;在这种情况下，焓值约为800 kj·mol^-1[51.]。这δ.H° calculated in this work was 21.75 kJ mol^-1·K.^-1，表明吸附过程由物理吸附控制。

Positive value ofδ.S.°（87.33 kj·mol^-1）indicates that the degrees of freedom increase at the solid-liquid interface during the adsorption of boron onto magnesium oxide particles.

4。结论

Equilibrium, kinetics, and thermodynamic studies for the adsorption of boron onto magnesium oxide powder were carried out.

这experimental data of adsorption were conducted by the Langmuir, Freundlich, and DR models, wherein the Freundlich isotherm was found to have a better fit for the equilibrium data for adsorption of boron under ambient temperature (25°C) and at higher temperatures (40°C and 50°C), respectively.

一种dditionally, the investigation of the kinetics of the overall adsorption process was conducted for the pseudo-first-order kinetic and pseudo-second-order kinetic models. Results show that the pseudo-second-order kinetic model generates the best fit to all experimental data. Such result suggests that the adsorption process at these temperatures seems to occur in two stages due to the two straight slopes obtained through the application of the pseudo-first-order kinetic model, which is confirmed by the adjustment of the results to the pseudo-second-order model.

计算的激活能量（）was 45.54 kJ·mol^-1，它在正常范围外略微略微（8-40kJ·mol^-1）for a typical physical adsorption process.

计算的值δ.G° andδ.H° were −4161.43 kJ·mol^-1和21.75 kj·mol^-1， 分别。这se values confirm the spontaneous and endothermic nature of the process and also suggest a physical adsorption process.

数据可用性

这boron analysis data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

提交人声明有关本文的出版物没有利益冲突。

一种cknowledgments

这funding for this research was provided by the Research and Development Center of Petrobras and the National Council for Scientific and Technological Research of Brazil (CNPq). The authors thank Mariana Lima for assistance during the experimental work.

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