CN111537400B - Method for online determination of fractal dimension of particulate matter in water - Google Patents
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Abstract
本发明公开了一种在线测定水中颗粒物分形维数的方法，属于水中颗粒物检测技术领域，旨在解决现有方法在线分析能力不足等问题。本发明利用连接有探头的电化学阻抗分析仪对水中颗粒物进行在线分析。在测试时无需对样品进行特殊处理，仅将电极探头插入待测颗粒悬浮液进行频率扫描测定复阻抗模量，并对得到的复阻抗模量进行校正处理。在确定的分形区间内根据建立的复阻抗模量与扫描频率间的无标度模型提取出颗粒物的分形维数。与现有方法相比，本发明适用的颗粒物浓度范围较宽，不受待测颗粒物及分散相的折射率和颜色的影响，且抗杂质污染的能力较强，设备维护相对简单，更能满足工业生产运行时水中颗粒物实时分析控制的需求。
The invention discloses an online method for measuring the fractal dimension of particulate matter in water, belongs to the technical field of particulate matter detection in water, and aims to solve the problems of insufficient online analysis ability of the existing method. The invention utilizes an electrochemical impedance analyzer connected with a probe to carry out on-line analysis on the particles in water. No special treatment is required for the sample during the test, only the electrode probe is inserted into the particle suspension to be tested for frequency scanning to measure the complex impedance modulus, and the obtained complex impedance modulus is corrected. The fractal dimension of the particles is extracted according to the scale-free model between the complex impedance modulus and the scanning frequency in the determined fractal interval. Compared with the existing method, the present invention is applicable to a wide range of particle concentration, is not affected by the refractive index and color of the particle to be measured and the dispersed phase, and has a strong ability to resist impurity pollution, relatively simple equipment maintenance, and can better meet The demand for real-time analysis and control of particulate matter in water during industrial production operation.
Description
所属技术领域Technical Field
本发明涉及水中颗粒物检测技术领域，具体的说是一种在线测定水中颗粒物分形维数的方法。The invention relates to the technical field of particle detection in water, in particular to a method for online determination of fractal dimension of particles in water.
背景技术Background Art
分形维数是表示颗粒物不规则程度的一种量度，其大小能反映颗粒物占据相应空间的程度，表示颗粒物的密实性。故其在表征颗粒物性质，控制颗粒物相关的工业过程中发挥着重要作用。Fractal dimension is a measure of the irregularity of particles. Its size can reflect the degree to which particles occupy the corresponding space and the density of particles. Therefore, it plays an important role in characterizing the properties of particles and controlling industrial processes related to particles.
目前，测定水中颗粒物分形维数的方法主要有显微图像法、流变法、自由沉降法及光散射法。然而这些方法尚存在缺陷，难以满足工业过程中实时分析控制的需求。其中显微图像法主要通过光学显微镜或电子显微镜提取单个颗粒的面积、周长及半径，从而计算出颗粒的分形维数。但是该方法反映的是单个颗粒物的分形特征，测试时需要颗粒群中的大量样本才能保证结果的准确性。流变法需要制备不同浓度的悬浮液样品，测试前的准备工作耗时较长。自由沉降法则需要在特定条件(自由沉降)下对颗粒的沉降速率进行测定。因此这些方法都难以在线快速反映颗粒物的分形特征。光散射法是目前应用最多的测试方法，在测试过程中通过变换不同的散射波矢，得到不同的散射强度。根据散射强度与波矢之间的无标度模型可计算出颗粒物的分形维数。该方法具有分析速度快，可在线的特点。然而，光散射法所适用的水中颗粒物浓度窗口较窄，不适用于浓稠的体系，且容易受颗粒物折射率及分散相颜色等因素干扰，在实际应用过程中光室的耐污性较差。这些问题的存在限制了该方法在工业过程中的应用范围。At present, the main methods for determining the fractal dimension of particles in water are microscopic imaging, rheological method, free sedimentation method and light scattering method. However, these methods still have defects and are difficult to meet the needs of real-time analysis and control in industrial processes. Among them, the microscopic imaging method mainly extracts the area, perimeter and radius of a single particle through an optical microscope or an electron microscope to calculate the fractal dimension of the particle. However, this method reflects the fractal characteristics of a single particle, and a large number of samples in the particle group are required to ensure the accuracy of the results during the test. The rheological method requires the preparation of suspension samples of different concentrations, and the preparation work before the test is time-consuming. The free sedimentation method requires the determination of the sedimentation rate of the particles under specific conditions (free sedimentation). Therefore, these methods are difficult to quickly reflect the fractal characteristics of particles online. The light scattering method is currently the most widely used test method. During the test, different scattering intensities are obtained by transforming different scattering wave vectors. The fractal dimension of the particle can be calculated based on the scale-free model between the scattering intensity and the wave vector. This method has the characteristics of fast analysis speed and can be online. However, the light scattering method is applicable to a narrow window of particle concentration in water, is not suitable for thick systems, and is easily affected by factors such as the refractive index of particles and the color of the dispersed phase. In practical applications, the light chamber has poor stain resistance. These problems limit the scope of application of this method in industrial processes.
发明内容Summary of the invention
针对现有技术的以上缺陷，本发明提供了一种在线测定水中颗粒物分形维数的方法，其目的是绕过现有方法的不足，利用连接有探头的电学设备在线测量水中颗粒物频率扫描时的电学特征，根据建立的模型，获取颗粒物的结构信息，提取颗粒物的分形维数。In view of the above defects of the prior art, the present invention provides a method for online determination of the fractal dimension of particles in water, the purpose of which is to bypass the shortcomings of the existing method, use an electrical device connected to a probe to measure the electrical characteristics of particles in water during frequency scanning online, obtain the structural information of the particles according to the established model, and extract the fractal dimension of the particles.
本发明可通过如下技术途径实现：The present invention can be achieved through the following technical approaches:
包括，用连接有电导电极的商业电化学阻抗仪对颗粒物悬浊液进行测试，在测试时无需对样品进行特殊处理，仅将电极探头插入待测颗粒悬浮液进行频率扫描测定复阻抗模量，并对得到的复阻抗模量进行校正处理，根据建立的校正后复阻抗模量与扫描频率间的无标度模型在确定的分形区间内提取出颗粒物的分形维数。The method includes testing a particle suspension using a commercial electrochemical impedance meter connected to a conductivity electrode. No special treatment of the sample is required during the test. The electrode probe is only inserted into the particle suspension to perform a frequency scan to determine the complex impedance modulus, and the obtained complex impedance modulus is corrected. The fractal dimension of the particle is extracted within a determined fractal interval based on a scale-free model between the corrected complex impedance modulus and the scanning frequency.
进一步地，所述颗粒物悬浊液样品的浓度范围为1mg/L-100g/L，测定时温度保持恒定，电化学阻抗仪施加的正弦电压范围为1-1000mV，扫描频率范围为0.1Hz-10 MHz。Furthermore, the concentration range of the particle suspension sample is 1 mg/L-100 g/L, the temperature is kept constant during the measurement, the sinusoidal voltage applied by the electrochemical impedance spectroscopy instrument is in the range of 1-1000 mV, and the scanning frequency range is 0.1 Hz-10 MHz.
进一步地，所述校正后的复阻抗模量等于每个扫描频率下对应的复阻抗模量减去最高频率下的复阻抗模量。Furthermore, the corrected complex impedance modulus is equal to the complex impedance modulus corresponding to each scanning frequency minus the complex impedance modulus at the highest frequency.
进一步地，所述建立的校正后复阻抗模量与扫描频率间的无标度模型为：Furthermore, the established scale-free model between the corrected complex impedance modulus and the scanning frequency is:
式中，|Zc|为校正后的复阻抗模量，f为扫描频率，Df为水中颗粒物的分形维数。Where |Z c | is the corrected complex impedance modulus, f is the scanning frequency, and D f is the fractal dimension of particles in water.
所述提取颗粒物分形维数的方法为：以|Zc|的对数值为Y轴，以扫描频率f的对数值为X轴作图，在确定的分形区间内用线性回归分析对图进行拟合，将所得斜率带入|Zc|与f间的无标度模型，即可求得颗粒物的分形维数。The method for extracting the fractal dimension of the particle is: plotting a graph with the logarithm of |Z c | as the Y axis and the logarithm of the scanning frequency f as the X axis, fitting the graph with linear regression analysis within a determined fractal interval, and bringing the obtained slope into a scale-free model between |Z c | and f to obtain the fractal dimension of the particle.
其中，所述分形区间为校正后的复阻抗模量的对数值随频率的对数值增加而线性下降的频率区间。The fractal interval is a frequency interval in which the logarithmic value of the corrected complex impedance modulus decreases linearly with the increase of the logarithmic value of the frequency.
本发明的有益效果是：The beneficial effects of the present invention are:
本发明提出了一种在线测量水中颗粒物分形维数的新方法，与目前现有方法相比，本发明适用的颗粒物浓度范围较宽，不受待测颗粒物及分散相的折射率和颜色的影响，且由于没有光路系统，抗杂质污染的能力较强，设备维护相对简单，更能满足工业生产运行时水中颗粒物实时分析控制的需求。The present invention proposes a new method for online measurement of fractal dimension of particles in water. Compared with the current existing methods, the present invention is applicable to a wider range of particle concentrations and is not affected by the refractive index and color of the particles to be measured and the dispersed phase. In addition, since there is no optical path system, the ability to resist impurity pollution is strong, the equipment maintenance is relatively simple, and it can better meet the needs of real-time analysis and control of particles in water during industrial production.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
附图1是本发明所述的水中颗粒物悬浊液分形维数测定示意图。FIG1 is a schematic diagram of the fractal dimension determination of a suspension of particulate matter in water according to the present invention.
图中：1—恒温器、2—电导电极、3—颗粒物悬浊液、4—商业电化学阻抗仪、5—电化学阻抗仪与电极间的连接导线。In the figure: 1—thermostat, 2—conductivity electrode, 3—particle suspension, 4—commercial electrochemical impedance spectroscopy, 5—connecting wires between the electrochemical impedance spectroscopy and the electrodes.
附图2是本发明所述的分形区间的确定示意图。FIG2 is a schematic diagram of determining the fractal interval according to the present invention.
具体实施方式DETAILED DESCRIPTION
下面结合附图及实施例对本发明进行详细说明，但所涉及附图及实施例仅是范例性的，并不对本发明的范围构成任何限制。本领域技术人员应该理解的是，在不偏离本发明的精神和范围下可以对本发明技术方案的细节和形式进行修改或替换，但这些修改和替换均落入本发明的保护范围内。The present invention is described in detail below in conjunction with the accompanying drawings and embodiments, but the drawings and embodiments involved are only exemplary and do not constitute any limitation to the scope of the present invention. It should be understood by those skilled in the art that the details and forms of the technical solution of the present invention can be modified or replaced without departing from the spirit and scope of the present invention, but these modifications and replacements all fall within the protection scope of the present invention.
校正后的复阻抗模量的获取：首先将具有频率扫描功能的商业电化学阻抗分析仪连接上电导率电极作为在线测试的工具。所述阻抗仪优选为日置IM3570，其性能参数介绍如表1所示。所述电导电极优选为Tetracon 325电极，其主要性能参数介绍如表2所示。Acquisition of the corrected complex impedance modulus: First, a commercial electrochemical impedance analyzer with a frequency scanning function is connected to a conductivity electrode as an online testing tool. The impedance analyzer is preferably Hioki IM3570, and its performance parameters are shown in Table 1. The conductivity electrode is preferably a Tetracon 325 electrode, and its main performance parameters are shown in Table 2.
表1阻抗分析仪的主要性能参数表Table 1 Main performance parameters of impedance analyzer
表2电导电极主要性能参数Table 2 Main performance parameters of conductivity electrode
如图1所示，将电导电极作为探头插入待测颗粒物悬浊液中进行频率扫描，探头插入深度应保证样品没过电极的接触圆片。悬浊液浓度范围为1mg/L-100g/L。扫描时阻抗仪施加1-1000mV正弦电压，扫描频率为0.1Hz-10 MHz，并记录不同频率下的复阻抗模量，采集点数为201。为减小悬浮液电导率的差异带来的影响，所得各扫描频率下的复阻抗模量需扣除最高频率下的复阻抗模量进行校正。As shown in Figure 1, the conductivity electrode is inserted as a probe into the particle suspension to be tested for frequency scanning. The probe insertion depth should ensure that the sample does not pass the contact disc of the electrode. The concentration range of the suspension is 1mg/L-100g/L. During the scan, the impedance meter applies a 1-1000mV sinusoidal voltage, the scanning frequency is 0.1Hz-10 MHz, and records the complex impedance modulus at different frequencies. The number of collection points is 201. In order to reduce the impact of the difference in the conductivity of the suspension, the complex impedance modulus obtained at each scanning frequency needs to be corrected by deducting the complex impedance modulus at the highest frequency.
分形区间的确定：对校正后的复阻抗模量及频率分别做对数转换并作图，如图2所示，当校正后的复阻抗模量的对数值随频率的对数值增加而线性下降时所对应的频率区间即为确定的分形区间。Determination of fractal interval: Logarithmic transformation is performed on the corrected complex impedance modulus and frequency, respectively, and a graph is plotted, as shown in FIG2 . When the logarithmic value of the corrected complex impedance modulus decreases linearly with the increase in the logarithmic value of the frequency, the corresponding frequency interval is the determined fractal interval.
无标度模型的建立：假设水中的每个颗粒都由若干个初级粒子构成。在交流电场的一定频率范围内，当频率变化时，电子移动区域内所涉及的初级粒子个数也发生变化。若将交流电场的扫描频率定义为标尺，则依据分形理论，在一定尺度下，不论标尺变大或变小，电子移动区域内的初级粒子个数都具有自相似性。因此可得Establishment of scale-free model: Assume that each particle in water is composed of several primary particles. Within a certain frequency range of the AC electric field, when the frequency changes, the number of primary particles involved in the electron movement region also changes. If the scanning frequency of the AC electric field is defined as the scale, then according to fractal theory, under a certain scale, no matter whether the scale becomes larger or smaller, the number of primary particles in the electron movement region has self-similarity. Therefore, it can be obtained
式中，|Zc|为校正后的复阻抗模量，f为扫描频率，Df为颗粒的分形维数。Where |Z c | is the corrected complex impedance modulus, f is the scanning frequency, and D f is the fractal dimension of the particle.
解方程提取分形维数：Solve the equation to extract the fractal dimension:
对上述模型两边取对数可得Taking the logarithm of both sides of the above model, we can get
其中，C为常数。Where C is a constant.
在确定的分形区间内，以lg|Zc|为Y轴，以lgf为X轴作图，并用线性回归分析进行拟合得出斜率k。In the determined fractal interval, a graph is drawn with lg|Z c | as the Y-axis and lgf as the X-axis, and the slope k is obtained by fitting using linear regression analysis.
依据上述建立的模型，有According to the above-mentioned model, we have
解上述方程可得颗粒物的分形维数Df。Solving the above equation gives the fractal dimension D f of the particles.
由于分形区间的确定、解方程提取分形维数等步骤均可通过编程实现，故在具体实施时仅需将测试探头插入待测悬浊液获取频率扫描时的复阻抗模量并进行校正，即可通过设计好的程序步骤在线反馈出水中颗粒物的分形维数。Since the steps of determining the fractal interval and solving equations to extract the fractal dimension can all be achieved through programming, in the specific implementation, it is only necessary to insert the test probe into the suspension to be tested to obtain the complex impedance modulus during frequency scanning and perform correction, and the fractal dimension of the particles in the water can be fed back online through the designed program steps.
下面采用以下实施例对本发明进行进一步的说明：The present invention is further described below by using the following examples:
实施例一：Embodiment 1:
从北京某再生水厂(记为再生水厂1)日处理水量为10万吨的膜生物反应器中取活性污泥(记为污泥1)作为待测颗粒物。污泥浓度为17.9g/L。其他测定过程与具体实施方式中所述一致。得到的分形区间内的lg|Zc|与lgf如表3所示。得到的污泥1的分形维数为2.534。Activated sludge (referred to as sludge 1) was taken from a membrane bioreactor with a daily water treatment capacity of 100,000 tons in a Beijing reclaimed water plant (referred to as reclaimed water plant 1) as the particulate matter to be measured. The sludge concentration was 17.9 g/L. The other measurement processes were consistent with those described in the specific implementation. The obtained lg|Z c | and lgf in the fractal interval are shown in Table 3. The fractal dimension of the obtained sludge 1 was 2.534.
实施例二：Embodiment 2:
从北京某再生水厂(记为再生水厂2)日处理水量为20万吨的厌氧/缺氧/好氧生物反应工艺中取剩余活性污泥(记为污泥2)作为待测颗粒物。污泥浓度为18.1g/L。其他测定过程与具体实施方式中所述一致。得到的分形区间内的lg|Zc|与lgf如表3所示。得到的污泥2的分形维数为2.362。The residual activated sludge (referred to as sludge 2) was taken from an anaerobic/anoxic/aerobic biological reaction process of a Beijing reclaimed water plant (referred to as reclaimed water plant 2) with a daily water treatment capacity of 200,000 tons as the particulate matter to be measured. The sludge concentration was 18.1 g/L. The other measurement processes were consistent with those described in the specific implementation. The obtained fractal interval lg|Z c | and lgf are shown in Table 3. The fractal dimension of the obtained
实施例三：Embodiment three:
从北京某再生水厂(记为再生水厂3)日处理水量为100万吨的厌氧/好氧生物反应工艺中取剩余活性污泥(记为污泥3)作为待测颗粒物。污泥浓度为18g/L。其他测定过程与具体实施方式中所述一致。得到的分形区间内的lg|Zc|与lgf如表3所示。得到的污泥3的分形维数为2.552。The residual activated sludge (referred to as sludge 3) was taken from an anaerobic/aerobic biological reaction process of a Beijing reclaimed water plant (referred to as reclaimed water plant 3) with a daily water treatment capacity of 1 million tons as the particulate matter to be measured. The sludge concentration was 18 g/L. The other measurement processes were consistent with those described in the specific implementation. The obtained fractal interval lg|Z c | and lgf are shown in Table 3. The fractal dimension of the obtained
实施例四：Embodiment 4:
从北京某再生水厂(记为再生水厂4)日处理水量为20万吨的氧化沟生物反应工艺中取剩余活性污泥(记为污泥4)作为待测颗粒物。污泥浓度为18.5g/L。其他测定过程与具体实施方式中所述一致。得到的分形区间内的lg|Zc|与lgf如表3所示。得到的污泥4的分形维数为2.5。The residual activated sludge (referred to as sludge 4) was taken from the oxidation ditch biological reaction process of a Beijing reclaimed water plant (referred to as reclaimed water plant 4) with a daily water treatment capacity of 200,000 tons as the particulate matter to be measured. The sludge concentration was 18.5 g/L. The other measurement processes were consistent with those described in the specific implementation method. The obtained fractal interval lg|Z c | and lgf are shown in Table 3. The fractal dimension of the obtained
实施例五：Embodiment five:
制备经聚丙烯酰胺交联的氢氧化铁凝胶(FHG-PAM)颗粒悬浮液作为待测颗粒物。颗粒浓度为3.25g/L。其他测定过程与具体实施方式中所述一致。得到的分形区间内的lg|Zc|与lgf如表3所示。得到的FHG-PAM的分形维数为2.564。A suspension of ferric hydroxide gel (FHG-PAM) particles cross-linked with polyacrylamide was prepared as the particles to be tested. The particle concentration was 3.25 g/L. The other measurement processes were consistent with those described in the specific implementation. The obtained lg|Z c | and lgf within the fractal interval are shown in Table 3. The fractal dimension of the obtained FHG-PAM was 2.564.
实施例六：Embodiment six:
制备阳离子水凝胶(CH)颗粒悬浮液作为待测颗粒物。颗粒浓度为0.2g/L。其他测定过程与具体实施方式中所述一致。得到的分形区间内的lg|Zc|与lgf如表3所示。得到的CH的分形维数为2.132。A cationic hydrogel (CH) particle suspension was prepared as the particle to be tested. The particle concentration was 0.2 g/L. The other measurement processes were consistent with those described in the specific implementation. The obtained lg|Z c | and lgf within the fractal interval are shown in Table 3. The obtained fractal dimension of CH was 2.132.
表3实施例中测试得到的分形区间内的lg|Zc|与lgfTable 3 lg|Z c | and lgf in the fractal interval obtained by testing in the embodiment
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