MT-Class-6-Summary

MSubbu begins the class by discussing the importance of regularly accessing site materials and spending at least one hour on studies despite busy schedules. He then introduces the day's topic, which is reviewing representative simple questions from mass transfer, covering various subtopics including diffusion, interface mass transfer, absorption, distillation, extraction, humidification, and drying. MSubbu mentions that the class materials are available on the GATE Course page and that they will discuss about 20 questions, spending approximately one to one and a half minutes per question.

The discussion focuses on diffusion in binary mixtures, specifically diffusion through non-diffusing components and equimolar countercurrent diffusion. MSubbu explains the equations for diffusion in gases and liquids, highlighting the relationship between concentration and pressure. He then discusses how diffusivity varies with pressure, temperature, and molecular weight in gases and liquids. MSubbu concludes by comparing diffusion coefficients in gases, liquids, and solids, noting that diffusivity is highest in gases, about 10,000 times lower in liquids, and even lower in solids.

The discussion focuses on gas absorption and the conditions that lead to gas film control. MSubbu explains that for gas film control to occur, the gas solubility in the liquid should be high, and the liquid-side mass transfer coefficient should be much higher than the gas-side coefficient. He emphasizes that under these conditions, the overall gas phase resistance is primarily due to the gas film resistance. MSubbu also mentions that to improve gas film-controlled processes, one should work on reducing gas film resistance or choose appropriate equipment.

MSubbu discusses various analogies in heat and mass transfer, focusing on Reynolds Analogy, Chilton-Colburn Analogy, and their applications. He explains that Reynolds Analogy is a simplified form of Chilton-Colburn Analogy, applicable mainly for gases in turbulent flow when the Prandtl number is approximately one. MSubbu then elaborates on the Colburn j-factor for mass transfer, relating it to Sherwood, Reynolds, and Schmidt numbers. He concludes by comparing thermal, mass, and momentum boundary layer thicknesses, explaining how they relate to Prandtl and Schmidt numbers for different fluids.

The discussion focuses on absorption operations in chemical engineering. MSubbu explains that to increase the absorption factor, the slope of the equilibrium line should decrease. He emphasizes that low temperature and high pressure are favorable conditions for absorption, as they lead to higher solubility of gases in liquids. MSubbu uses the example of dissolved oxygen in water to illustrate this concept, noting that in summer, fish may die due to reduced oxygen solubility at higher temperatures. He concludes by contrasting absorption with stripping operations, which require opposite conditions of high temperature and low pressure.

The discussion focuses on various aspects of distillation and mass transfer operations. MSubbu explains that lower NTU (Number of Transfer Units) and HTU (Height of Transfer Unit) values indicate easier separation and better performance. He discusses how HTU is related to gas flow rate, mass transfer coefficient, and interfacial area. MSubbu then explains the concept of \(q\)-line in binary distillation, describing how to calculate its slope when the feed contains a mixture of vapor and liquid. He demonstrates that for a feed with 40% vapor, the slope of the \(q\)-line is \(-1.5\), and illustrates how different feed conditions affect the \(q\)-line's position on an \(x\)-\(y\) diagram.

MSubbu explains the effects of increasing the reflux ratio in a distillation column. He states that increasing the reflux ratio generally improves product purity in both the distillate and residue, but reduces throughput and increases operating costs due to higher condensation and reboiling requirements. MSubbu also discusses the relationship between reflux ratio, number of trays, and reboiler heat load, noting that minimum reflux implies infinite trays and minimum reboiler load. Finally, he explains that when scaling up a distillation column, the number of trays and reflux ratio remain unchanged, while feed and product flow rates increase proportionally.

MSubbu explains how to read compositions from a triangular chart, focusing on points P, Q, and R. He demonstrates that for point \(k\), Q is 12.5%, P is 62.5%, and R is 25%. MSubbu then discusses the lever arm rule for extraction, explaining how to calculate raffinate and extract amounts using given distances and quantities. He also relates this concept to the PVT behavior of pure components in thermodynamics, using the analogy of vapor-liquid equilibrium and dryness fraction to help remember the lever arm rule.

MSubbu discusses ways to reduce solvent requirements in extraction processes. He explains that adding an ideal co-current stage or doubling the residence time would not improve efficiency as equilibrium is already reached in a single stage. MSubbu suggests that using a countercurrent process or a solvent with a higher partition coefficient could effectively reduce solvent requirements. He concludes that, here doubling the distribution coefficient is the expected method to achieve this goal.

The discussion covers various aspects of psychrometric charts and drying processes. MSubbu explains the different processes represented on a psychrometric chart, including heating, humidification, and cooling. He discusses the concepts of relative humidity and percentage humidity, clarifying the difference between them. The conversation then shifts to drying operations, explaining equilibrium moisture content, bound and unbound moisture, and the temperature changes that occur during the drying process. MSubbu also mentions that he will address a student's question about absorption factors in a future class.