汽液平衡
English
Condividere
Panoramica
资料来源: 迈克尔 g. 本顿和克里先生, 路易斯安那州立大学化学工程系, 巴吞鲁日, 洛杉矶
蒸汽-液体平衡是最重要的工程应用, 如蒸馏, 环境建模, 和一般工艺设计。了解混合物中组分的相互作用对于设计、操作和分析这种分离器是非常重要的。活性系数是一种将分子相互作用与混合物组成联系起来的极好工具。找到分子相互作用参数允许未来预测的活动系数的混合物使用模型。
汽液平衡是化学工业中常见过程的关键因素, 如蒸馏。蒸馏是通过沸点来分离液体的过程。将液体混合物送入蒸馏单元或柱中, 然后煮沸。汽液平衡数据是有用的, 以确定如何液体混合物将分离。因为液体有不同的沸点, 一液体将煮沸入蒸气和上升在专栏, 而其他将停留作为液体和排泄通过单位。这一过程在各种行业中非常重要。
本实验采用汽液平衡仪和气相色谱法, 得到了甲醇、异丙醇、去离子水中各种组分的混合物的活性系数。此外, 还将利用威尔逊方程和活动系数确定系统的二元相互作用参数。
Principi
汽液平衡是一种状态, 其中纯组分或混合物存在于液体和蒸气相, 具有机械和热平衡, 在两相之间没有净传质。蒸气和液体被重力和热量分开 (图 1)。液体混合物入系统 , 被投入真空状态与真空泵浦。蒸气凝结, 并返回与液体混合, 然后传递回沸腾室。沸点的差异会导致混合物的分离。水的沸点比增加的组分高, 因此挥发性组分开始蒸发。
图 1: 仪器的描述
活动系数的定义是一个组分的逸在一个实际的混合物的比例, 以逸的理想溶液的相同成分。逸是一种用于显示标准状态下化学势的差异的属性。气相 fugacities 可以用一个逸系数来表示 [φ: fiV = φi y我f i0V , 与 yi = 摩尔分数 i 在蒸气阶段, 和 fi0V = 蒸气标准状态逸 (纯组分蒸气的逸在 T 和 P)。对于低压力, 在本实验中, φ i = 1 和 fi0V = p. 液相 fugacities 可以用一个活动系数γi: fiL = γ i xi f0L , 具有 xi = 在液相中 i 的摩尔分数, 和 fi0L = 液体标准状态逸。
在饱和压力 (pis), 纯组分液体逸将是 Pis, 因为纯净的蒸气和液体在平衡。由于液体 fugacities 仅是压力的微弱函数, 我们可以在 T 和 p (fi0L) 上将纯组分液体逸近似为 pi, 只要 pis和 p 之间的差异不大。这种近似通常被称为 “忽略印校正”。如果实验者使用汽仪器来测量处于平衡状态的蒸气和液体的成分, 实验者可以直接计算所提供的活动系数来测量 p 和 t. 必须测量, 以确定 piS为所有 i。
汽装置的心脏, 在这个实验中用来确定混合物的成分, 是一种科特雷尔泵, 它将沸腾的液体 “吐出” 到一个井绝缘的平衡室。两个磁性操作的取样阀允许提取液体和冷凝气样品。一个大的水库有助于抑制系统中的压力脉冲, 作为关闭控制阀开关, 并由科特雷尔泵引起的波动。一个缓慢的泄漏可以用来创造一个平衡的空气的退出率和空气的输入率保持恒定的压力, 如果必要的。
一个类似的方法来解决汽液平衡是使用各种模型。拉乌尔定律、道尔顿定律和亨利定律都是能找到汽液平衡浓度数据的理论模型。所有三种模型都与部分压力、总压强和物质的摩尔分数的比例有关。威尔逊的方程式已被证明是准确的混溶液体, 而不是过于复杂。此外, 威尔逊的模型纳入活动系数, 以考虑偏离理想值。
Procedura
Risultati
The activity coefficients of the data do not show significant deviations from a mean value for each component (Table 1). This is as expected because for intermediate component compositions there are not large variations. However, components near 1 have γ's near 1. Low composition components have high γ's. Components highest in concentration in a mixture which will have a reduced deviation, therefore it will be closer to ideal (γ = 1). Components with lower concentrations in a mixture will have higher deviations, so their γ's will be greater than 1.
Table 1: Results of each sampling of the experimental data.
The data were fit to Wilson model parameters and the coefficients were calculated (Table 2). A simple reduction in the sum of squared residuals between experimental and Wilson equation (1) activity coefficients was used. This was achieved using Excel's solver function. The parity plot shown relates the Wilson's Equation model activity coefficients to the experimentally found activity coefficients. The experimental activity coefficients were calculated and graphically compared to the calculated model coefficients.
Table 2: Results of fitting the data to the Wilson model parameters.
(1)
The parameter values found were the best fit (Table 3). Ideally the correlation is along the y=x line; however, a significant correlation resembling the ideal scenario was found (Figure 2). The activity coefficients of the data did not show significant deviations from a mean value for each component, as expected. A reduction in the sum of squared residuals between experimental and Wilson equation activity coefficients was used with Excel's solver function. The parity plot relates the Wilson's Equation model activity coefficients to the experimentally found activity coefficients.
Table 3: Model parameters with water (a), MeOH (b), and IPA (c). The experimental values are compared to expected values.
Figure 2: Depiction of the correlation between the experimental activity coefficients and the model activity coefficients.
Applications and Summary
This experiment demonstrated the equilibration of methanol – isopropanol – water vapor-liquid mixtures at a constant P = 700 mm Hg and how to measure temperature and composition and calculate activity coefficients. The activity coefficients of the data did not significantly deviate from a mean value for each component, as expected. A reduction in the sum of squared residuals between experimental and Wilson equation activity coefficients was used with Excel's solver function. The parity plot relates the Wilson's Equation model activity coefficients to the experimentally found activity coefficients.
In the petroleum industry, distillation is the primary process for separation of petroleum products. Many oil refineries use distillation for crude oil1. Light hydrocarbons are separated from heavier particles, separating based on boiling points1. Heavy materials like gas oils collect in the lower plates, while light materials like propane and butane rise up1. Hydrocarbons, such as gasoline, jet, and diesel fuels, are separated1. This process is often repeated many times to fully separate and refine the products1. Refineries run these processes at steady state, constantly creating new products at maximum capacity, so efficiency is key1. Chemical engineers working on these processes focus on optimizing the efficiency of the production1.
Tray distillation columns are also used to separate a variety of chemical products. Ethanol is one such product. Through closely related processes, a variety of products such as fuel-grade ethanol, beer, and liquor can all be distilled2. Specific amounts of alcohol can be separated from water in order to create a specific proof2. This process is limited to reducing the percentage of water in the product, but cannot completely eliminate it2. In order to remove water completely, azeotropic distillation is required, which uses extractor chemicals to separate water from ethanol2.
Riferimenti
- About the Refinery." Processing & Refining Crude Oil. Chevron.com, n.d. Web. 17 Nov. 2016.
- Madson, PW. Ethanol Distillation: The Fundamentals. Cincinnati: Katzen International, n.d. Print. Accessed from Web. 01 Oct. 2016.
Trascrizione
Understanding the distribution of chemical components in both the vapor and liquid phase, called vapor-liquid equilibrium is essential to the design, operation, and analysis of many engineering processes. Vapor-liquid equilibrium or VLE is a state at which a pure component or mixture exists in both the liquid and vapor phases. The phases are at equilibrium meaning that there were no changes in the macroscopic properties of the system over time. Single component VLE is simple to visualize. Take for example water which is at equilibrium in the vapor and liquid phase at 100 degrees Celsius and one atm. Above this temperature water is a vapor. Below it, water is a liquid. However, engineers generally encounter processes with mixtures in equilibrium making the analysis of VLE more complex and therefore essential to process design. This video will illustrate the principles behind vapor-liquid equilibrium of mixtures and demonstrate how to analyze the VLE of a mixture in the laboratory. Finally, some applications of VLE in the chemical engineering field will be introduced.
When a heated mixture is in a vapor-liquid equilibrium, the vapor and liquid phases generally do not have the same composition. The substance with the lower boiling point will have a higher concentration in the vapor than the substance with the higher boiling point. Thus, engineers refer to components in each phase by their mole fraction where xi is the mole fraction of species i in the liquid and yi is the mole fraction of species i in the vapor phase. This relationship is often depicted using an xy curve like the one shown here for a mixture of two components which illustrates the relationship between each component in each phase. A starting point for all VLE calculations is the simple equilibrium criterion where the fugacity of the species in the vapor equals the fugacity of the species in the liquid. Fugacity is a property related to the exponential difference between the real and ideal gas Gibbs energies. The vapor phase fugacity is equal to the mole fraction of species i in the vapor phase times the pure component vapor fugacity. The expression can be simplified as the pure component vapor fugacity is approximately equal to pressure at low pressure. Liquid phase fugacities are expressed in terms of an activity coefficient, gamma. The activity coefficient is defined as the ratio of a component’s fugacity in an actual mixture to the fugacity of an ideal solution of the same composition. At the saturation vapor pressure the pure component liquid fugacity would equal the saturation vapor pressure because the pure vapor and liquid are in equilibrium there. Finally, since the liquid and vapor fugacities are equal, we can further simplify the relationship as shown which is also known as Raoult’s law. The saturation vapor pressure is often calculated using the Antoine equation where the constants A, B, and C are species-specific and can be found in the literature. Thus, if we measure the compositions of the vapor and liquid which are in equilibrium, we can directly calculate the activity coefficients by measuring temperature and pressure and therefore the saturation vapor pressure. In this experiment a ternary mixture of methanol, isopropyl alcohol and water will be investigated. Various compositions of the mixture are boiled in a VLE apparatus and the lower boiling point components vaporize and are collected in a separate container while the liquid gathers back into the initial sample vessel. Once equilibrium is reached, the liquid and condensed vapor fractions are collected and analyzed with gas chromatography. Using temperature and the liquid and vapor mole fractions the activity coefficients can be calculated. Now that you’ve been introduced to the concepts of VLE and the testing apparatus, let’s see how to carry out the experiment in the laboratory.
To start, drain any liquid out of the system into a waste flask. Keep in mind that the liquid may not completely drain. For the first run add a mixture of 50% methanol, 30% IPA and 20% water through the opening at the top. After filling the mixture, turn on the heater power and condenser water. The apparatus will require roughly 20 minutes to approach equilibrium. The system is now ready to begin the experiment.
When the sample begins boiling, release the stopper to vent the inert outlet of the system. Condensed vapor will start collecting. When equilibrium is reached, steady drips of condensed vapor and returns liquid should be observed. With the temperature stable to within 0.3 degrees for 10 minutes, collect about 1/2 milliliter of liquid in sample vials from both the condensed vapor and the boiling liquid. Drain the condensed vapor from the last sample. Then add a new sample consisting of either 20 milliliters of pure methanol or 50-50 methanol-isopropanol through the sample port. This will give a new overall composition. Reestablish the equilibrium as performed before, however expect a temperature difference from the previous sample. Repeat the equilibration and sampling procedure as before, and then collect the sample to be analyzed. Continue the experiment using different mixtures of the three components. 12 points are sufficient to determine the activity coefficients and the binary interaction coefficients. When all the mixtures have been run, shut down the system by turning off the heaters. When the apparatus begins to cool, shut off the condenser water. Finally measure the composition of each liquid and vapor sample with the gas chromatograph or GC.
Using the system temperature and the liquid and vapor mole fractions acquired from GC, calculate the activity coefficients. This first requires that the saturation pressure is calculated using the Antoine equation where the constants A, B and C for each component can be found in the literature. Now we can use the calculated activity coefficients to correlate the data to a model. We will use the Wilson equation for a ternary mixture which accounts for deviations from ideality in a mixture. The nine lambda constants are the Wilson constants which equal one when i equals j. For each ij pair, there are two different constants. Use a nonlinear regression and a standard sum of squares residual function to determine the six remaining Wilson constants using the mole fraction data from the experiment. The Wilson constants are then used to determine the expected activity coefficients for each component of each sample. Here we show the modeled activity coefficient plotted against the experimental activity coefficients. Ideally, the modeled and experimental activity coefficients would fall along the y equals x line. As you can see in general, the modeled and experimental values fit along this line showing that the model is a good fit to the real system.
Understanding and manipulating the vapor-liquid equilibrium of mixtures is a vital component to a range of processes especially separations. Distillation columns separate mixtures based on their volatility with different compositions of each component in the liquid and vapor phrases on each tray. The more volatile component is vaporized and collected at the top of the column, while the less volatile component remains liquid and is collected at the bottom. VLE data of the components of the mixture is used to determine the number of trays needed to achieve separation in a distillation column. This helps engineers optimize the separation process while keeping operating costs low. Another valuable separation technique using VLE is flash separation. Flash separation is based on the fact that a liquid at a pressure equal to or greater than its bubble point pressure flashes meaning that it partially evaporates when the pressure is reduced. The feed is preheated thus consisting of some liquid and some vapor in equilibrium. It then flows through a pressure reducing valve into the separator. The degree of vaporization and therefore the amount of the solute in the vapor or liquid phases depends on the initial state of the feed stream.
You’ve just watched Jove’s introduction to vapor-liquid equilibrium. You should now understand the concepts behind VLE, how it’s measured in the laboratory, and some of its uses in engineering processes. Thanks for watching.