91Ó°ÊÓ

A liquid mixture containing ethanol ( 55.0 wt\%) and the balance water enters a separation process unit at a rate of \(90.5 \mathrm{kg} / \mathrm{s}\). A technician draws samples of the two product streams leaving the separator and analyzes them with a gas chromatograph, obtaining values of 86.2 wt\% ethanol (Product Stream 1) and \(10.9 \%\) ethanol (Product Stream 2). The technician then reads a manometer attached to an orifice meter mounted in the pipe carrying Product Stream 1, converts the reading to a volumetric flow rate using a calibration curve, and converts that result to a mass flow rate using the average density of ethanol and water. The result is \(54.0 \mathrm{kg} / \mathrm{s}\). Finally, the technician calculates the mass flow rate of the second product stream using a material balance and reports the calculated product stream flow rates and compositions to you. You examine them, do some calculations, and reject them. (a) Draw and label a flow chart of the separation process. (b) Carry out the calculations that led you to reject the submitted results and explain how you knew the values were wrong. (c) List up to five possible reasons for the incorrect results. For each one, briefly state how you might determine whether it was in fact a cause of error and what you might do to correct it if it was.

Step by step solution

01

Drawing the Flowchart

Firstly, start by establishing a flowchart for the separation process. The flowchart comprises an inlet stream entering the system (90.5 kg/s of mixture containing 55 wt% ethanol), a separation unit where the ethanol-water mixture is divided into two streams – one concentrated in ethanol (Product Stream 1 with 86.2 wt% ethanol and flow rate 54.0 kg/s as measured by an orifice meter mounted in the pipe) and the other dilute ethanol stream (Product Stream 2 with 10.9 wt% ethanol, whose flow rate would be determined by material balance).

02

Calculation of Ethanol and Water Amount in Inlet Stream

Firstly, calculate the mass of ethanol and water in the inlet stream per second. Since it is given that the ethanol is 55% of the weight of the mixture entering, the amount of ethanol entering would be \(0.55*90.5=49.775 kg/s\). The balance is the water so amount would be \(90.5-49.775=40.725 kg/s\).

03

Calculation of Ethanol and Water Amount in Product Stream 1

Next, determine the amount of ethanol and water in product stream 1 per second. Given that the concentration of ethanol is 86.2%, the amount of ethanol in this stream is \(0.862*54.0=46.548 kg/s\). The balance is the water so that amount would be \(54.0-46.548= 7.452 kg/s\).

04

Calculation of Ethanol Amount in Product Stream 2

Next, determine the amount of ethanol in product stream 2 per second by performing a material balance around ethanol. According to conservation of mass, the total amount of ethanol entering the system should be equal to the total amount leaving. Therefore, the amount of ethanol in product stream 2 is \(49.775 - 46.548 = 3.227 kg/s\).

05

Calculation of Water Amount in Product Stream 2

Perform a similar material balance for water: the amount of water in product stream 2 is \(40.725 - 7.452= 33.273 kg/s\).

06

Calculation of Total Mass Flow Rates for each Product Stream

Product stream 1's mass flow rate is \(46.548 + 7.452 = 54.0 kg/s\), which matches the technician's measurement; yet Product stream 2's mass flow rate is \(3.227 + 33.273 = 36.5 kg/s\), which does not match the measured read because it was calculated incorrectly by the technician. This discrepancy leads to the rejection of the submitted results.

07

Potential Reasons for the Error

Several reasons could explain incorrect results. Some possible reasons include 1) The calibration curve for converting the manometer reading to volumetric flow rate may not be correct, 2) The average density used for converting volumetric flow rate to mass flow rate may not be accurate, 3) The gas chromatograph analysis could be inaccurate due to instrument error or mishandling of the sample, 4) Loss of ethanol or water to the environment due to evaporation or leakage during the process, 5) The manometer reading taken could be inaccurate. Each of these could be investigated further by checking calibration records, re-analyzing samples, visual inspections for leaks, and evaluating the conditions and procedures used by the technician.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Process Separation

Chemical process separation is a fundamental part of the chemical industry, designed to separate mixtures of compounds into distinct components. This can be accomplished through a variety of methods such as distillation, filtration, or extraction. In the context of the textbook exercise, an ethanol-water mixture undergoes separation to yield two distinct streams: one with a high concentration of ethanol and the other with a low concentration. Understanding how separations work and the principles behind them, like the equilibrium between components and the conservation of mass, is crucial for engineers and technicians in optimizing these processes.

Mass Flow Rate

The mass flow rate in chemical engineering refers to the amount of mass passing through a given point in a system per unit of time. It's denoted as kg/s in the metric system and is a critical parameter in the design and operation of most chemical processes. In the exercise, the mass flow rates of the product streams from the separation unit are focal points of the analysis. Accurate calculation of the mass flow rates is essential in ensuring that the inputs and outputs of the process balance, which is the basis of material balance calculations in process engineering.

Ethanol-Water Separation

Ethanol-water separation is often carried out using distillation, a process that takes advantage of the difference in boiling points between the two compounds. However, the separation is not perfect, and the process must be evaluated to ensure efficiency. With a binary mixture like ethanol and water, the separation strives to produce one stream enriched in ethanol and another in water. Inaccuracies in the separation process could lead to incorrect compositions or flow rates, leading to operational inefficiencies and potential product losses.

Flowchart Diagramming

Flowchart diagramming is an essential tool in process engineering for visualizing the steps and operations within a chemical process. Flowcharts use symbols and arrows to depict the flow of materials and transformation steps in the process. Properly drawing and labeling a flowchart, as required in part (a) of the exercise, helps process operators, engineers, and technicians to understand and communicate the process flow clearly. It serves as a blueprint that outlines how inputs are processed to yield desired outputs.

Process Unit Operation

A process unit operation refers to a fundamental step in a processing system where a physical or chemical change happens. Common unit operations in chemical engineering include separation, reaction, heat exchange, and mass transfer. Each operation requires careful design and control to meet specific objectives. In the case of the textbook exercise, the separation process unit operation focuses on dividing the ethanol-water mixture into distinct streams with different ethanol concentrations.

Material Balance Error Analysis

Material balance error analysis involves inspecting the inputs and outputs of a process to ensure the law of conservation of mass is satisfied. When the numbers don't add up, as in the erroneous technician's data reported in the exercise, it indicates possible measurement errors, process leaks, or procedural mistakes. Identifying and addressing these issues is vital for reliable operation and credibility of the process performance. Error analysis often starts with a return to the basic principles, measuring and validating each step of the process, from raw data collection through to the final calculation of flow rates and compositions.