91Ó°ÊÓ

The fresh feed to an ammonia production process contains nitrogen and hydrogen in stoichiometric proportion, along with an inert gas (I). The feed is combined with a recycle stream containing the same three species, and the combined stream is fed to a reactor in which a low single-pass conversion of nitrogen is achieved. The reactor effluent flows to a condenser. A liquid stream containing essentially all of the ammonia formed in the reactor and a gas stream containing all the inerts and the unreacted nitrogen and hydrogen leave the condenser. The gas stream is split into two fractions with the same composition: one is removed from the process as a purge stream, and the other is the recycle stream combined with the fresh feed. In every stream containing nitrogen and hydrogen, the two species are in stoichiometric proportion. (a) Let \(x_{10}\) be the mole fraction of inerts in the fresh feed, \(f_{\mathrm{sp}}\) the single-pass conversion of nitrogen (and of hydrogen) in the reactor, and \(y_{p}\) the fraction of the gas leaving the condenser that is purged (mol purged/mol total). Taking a basis of 1 mol fresh feed, draw and fully label a process flowchart, incorporating \(x_{10}, f_{\mathrm{sp}},\) and \(y_{\mathrm{p}}\) in the labeling to the greatest possible extent. Then, assuming that the values of these three variables are given, write a set of equations for the total moles fed to the reactor \(\left(n_{\mathrm{r}}\right),\) moles of ammonia produced \(\left(n_{\mathrm{p}}\right),\) and overall nitrogen conversion \(\left(f_{\mathrm{ov}}\right) .\) Each equation should involve only one unknown variable, which should be circled. (b) Solve the equations of Part (a) for \(x_{10}=0.01, f_{\mathrm{sp}}=0.20,\) and \(y_{\mathrm{p}}=0.10\) (c) Briefly explain in your own words the reasons for including (i) the recycle stream and (ii) the purge stream in the process design. (d) Prepare a spreadsheet to perform the calculations of Part (a) for given values of \(x_{10}, f_{\mathrm{sp}},\) and \(y_{\mathrm{p}} .\) Test it with the values in Part (b). Then in successive rows of the spreadsheet, vary each of the three input variables two or three times, holding the other two constant. The first six columns and first five rows of the spreadsheet should appear as follows:Summarize the effects on ammonia production \(\left(n_{\mathrm{P}}\right)\) and reactor throughput \(\left(n_{\mathrm{r}}\right)\) of changing each of the three input variables.

Step by step solution

01

Process Flow Chart Diagram

The first part of the exercise is to create a process flow chart incorporating the mole fraction of inerts in the fresh feed (\(x_{10}\)), the single-pass conversion of nitrogen (\(f_{\mathrm{sp}}\)), and the fraction of the gas leaving the condenser that is purged (\(y_{p}\)). This diagram will help you visualize the process and understand the interaction of each component within a unit operation set-up.

02

Equations for Variables

Given the values of \(x_{10}\), \(f_{\mathrm{sp}}\), and \(y_{p}\), develop equations to determine the total moles fed to the reactor (\(n_{\mathrm{r}}\)), moles of ammonia produced (\(n_{\mathrm{p}}\)), and overall nitrogen conversion (\(f_{\mathrm{ov}}\)). The equations look like this: \(n_r = 1/(1 - f_{sp}*(1 - y_p))\), \(n_p = f_{sp}*n_r*(1 - x_{10})\), \(f_{ov} = n_p/(1 - x_{10})\).

03

Solving Equations

Substitute the given values \(x_{10}=0.01, f_{\mathrm{sp}}=0.20, y_{p}=0.10\) into the equations to determine the corresponding \(n_r, n_p, f_{ov}\). Calculate each of these values by applying the corresponding formulas.

04

Understanding Process Design Reasons

Write a brief explanation regarding the reasons for including the recycle stream and the purge stream in the process design. In essence, the recycle stream serves to increase the conversion of nitrogen by reintroducing unreacted nitrogen and hydrogen back to the reactor. On the other hand, the purge stream is necessary to prevent the build-up of the inert gas, which does not react and thus accumulates over time.

05

Preparing and Testing Spreadsheet

Prepare a spreadsheet that would carry out calculations of part (a) for given values of \(x_{10}, f_{\mathrm{sp}}, y_{p}\) and test it with the values given in part (b). Add several rows in the spreadsheet where each of the three input variables \(x_{10}, f_{\mathrm{sp}}, y_{p}\) are individually varied while holding the other two variables constant. Analyze how changes in each of these variables affects ammonia production (\(n_{\mathrm{p}}\)) and reactor throughput (\(n_{\mathrm{r}}\)).

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Key Concepts

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

Ammonia Production Process

The production of ammonia is a critical process in the chemical industry, instrumental in creating fertilizers, plastics, and other vital materials. At the center of this process is the Haber-Bosch method, which combines nitrogen from the air with hydrogen (often derived from natural gas) to form ammonia (NH3) through a catalytic reaction under high pressure and temperature.

With the exercise in hand, we learned that the fresh feed to an ammonia production process contains nitrogen, hydrogen, and an inert gas. It's essential to note that the stoichiometry (the specific ratio of reactants) is crucial for optimizing the production and minimizing waste. This exercise delves into how different variables, such as the mole fraction of inerts in the fresh feed, affect the overall process and output, and this understanding is foundational for any chemical engineer working in this field.

Stoichiometric Calculations

Stoichiometry is the mathematical relationship between the relative quantities of reactants and products in chemical reactions. These calculations are pivotal as they ensure that the reactants are supplied in the correct proportions to maximize the yield of products while minimizing excess and waste.

In the given problem, stoichiometric proportion is highlighted by the condition that nitrogen (N) and hydrogen (H) are present in streams in a ratio that favors their reaction to produce ammonia. Stoichiometric calculations allow us to quantify how changes in the process variables affect the moles of ammonia produced, ensuring the efficiency of the overall production.

Process Flowchart

A process flowchart is an essential tool used to visually represent the sequence and interactions of various steps within a chemical process. It helps in understanding the flow of materials and energy throughout the system. When creating a process flowchart, it's important to include all the streams, process units, and the interactions between them.

In the exercise, the flowchart would incorporate the variables such as the mole fraction of inerts, the single-pass conversion of nitrogen, and the purge fraction. This visual representation aids in analyzing the changes in these variables and assists in troubleshooting and optimizing the ammonia production process.

Chemical Process Design

Chemical process design involves creating an efficient plan for transforming raw materials into desired products. It encompasses the choice of reactants, process conditions, and equipment that collectively contribute to the safety, efficiency, and sustainability of industrial operations.

In the context of the ammonia production problem, the inclusion of recycle and purge streams in the design is tailored to improve the yield and manage the accumulation of non-reactive species. Understanding the rationale behind process design elements, like recycle and purge streams, is crucial for making informed decisions in real-world chemical engineering scenarios.

Nitrogen Conversion

Nitrogen conversion refers to the amount of nitrogen that reacts to form ammonia in a single pass through the reactor. It's a measure of process efficiency. Low single-pass nitrogen conversion is common in industrial ammonia synthesis due to equilibrium limitations, and therefore, multiple passes or recycle streams are often necessary to achieve high overall conversion.

The exercise provides an opportunity to explore the variable of single-pass conversion and its impact on the overall nitrogen conversion. This understanding is essential for optimizing the reactor design and operating conditions, which are integral to the economic and environmental performance of the ammonia production process.

Recycle and Purge Streams

Recycle streams are used to feed unreacted reactants back into the reactor to improve conversion rates and economic efficiency. Conversely, purge streams help in removing inert gases or impurities that could accumulate in the system, which can negatively impact the reaction and catalyst performance.

The exercise introduces students to the concept of balancing these streams to maintain a steady-state operation. By adjusting the fraction of the gas leaving the condenser that is purged, one can influence the entire system's dynamics, including the total moles fed to the reactor and the moles of ammonia produced. This real-world practice is taught through the exercise, helping students appreciate the intricacies involved in designing and operating a chemical process.