91Ó°ÊÓ

Biodiesel fuel - a sustainable alternative to petroleum diesel as a transportation fuel- -is produced via the transesterification of triglyceride molecules derived from vegetable oils or animal fats. For every \(9 \mathrm{kg}\) of biodiesel produced in this process, \(1 \mathrm{kg}\) of glycerol, \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3},\) is produced as a byproduct. Finding a market for the glycerol is important for biodiesel manufacturing to be economically viable. A process for converting glycerol to the industrially important specialty chemical intermediates acrolein, \(C_{3} \mathrm{H}_{4} \mathrm{O},\) and hydroxyacetone (acetol), \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{2},\) has been proposed. $$\begin{array}{l}\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3} \rightarrow \mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}+2 \mathrm{H}_{2} \mathrm{O} \\ \mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3} \rightarrow \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{2}+\mathrm{H}_{2} \mathrm{O} \end{array}$$ The reactions take place in the vapor phase at \(325^{\circ} \mathrm{C}\) in a fixed bed reactor over an acid catalyst. The feed to the reactor is a vapor stream at \(325^{\circ} \mathrm{C}\) containing 25 mol\% glycerol, \(25 \%\) water, and the balance nitrogen. All of the glycerol is consumed in the reactor, and the product stream contains acrolein and hydroxyacctone in a 9: 1 mole ratio. Data for the process species are shown below. $$\begin{array}{|l|c|c|}\hline \text { Species } & \Delta \hat{H}_{\mathrm{f}}(\mathrm{kJ} / \mathrm{mol}) & C_{p}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right] \\ \hline \text { glycerol(v) } & -620 & 0.1745 \\ \hline \text { acrolein(v) } & -65 & 0.0762 \\\\\hline \text { hydroxyacetone(v) } & -372 & 0.1096 \\ \hline \text { water(v) } & -242 & 0.0340 \\\\\hline \text { nitrogen(g) } & 0 & 0.0291 \\ \hline\end{array}$$ (a) Assume a basis of 100 mol fed to the reactor, and draw and completely label a flowchart. Carry out a degree-of-freedom analysis assuming that you will use extents of reaction for the material balances. Then calculate the molar amounts of all product species. (b) Calculate the total heat added or removed from the reactor (state which it is), using the constant heat capacities given in the above table. (c) Assuming this process is implemented along with biodiesel production, how would you determine whether the biodiesel is an cconomically viable alternative to petroleum diesel? (d) If you do a degree-of-freedom analysis based on atomic species balances, you are likely to count one more equation than you have unknowns, and yet you know the system has zero degrees of freedom. Guess what the problem is, and then prove it.

Step by step solution

01

Flowchart and Degree-of-Freedom Analysis

First, construct a flowchart detailing the reactions, and label it with the reactants and products. Then, perform a degree of freedom analysis using the extents of the reactions. With 100 mol being fed into the reactor, you can calculate the molar amounts of the product species. In this system, there are two reactions, involving four species, therefore four independent equations can be found for the two unknown extent of reactions. Hence, the system has zero degree of freedom.

02

Molar Amounts Calculation

Let \(x\) and \(y\) represent the extents of the first and second reaction respectively. From the stoichiometry of the two reactions, we have \(x + y = 25\) mol (total glycerol reacted). We also know the product stream contains acrolein and hydroxyacetone in a 9:1 molar ratio, which constructs another equation \(x = 9y\). Solving these equations, we get \(x = 22.5\) mol and \(y = 2.5\) mol. Hence, the amounts of acrolein, hydroxyacetone and water produced are 22.5 mol, 2.5 mol and \(2x + y = 47.5\) mol, respectively, while the amount of nitrogen remains unchanged at 50 mol.

03

Total Heat Calculation

We can calculate the heat added or removed from the reactor using the heat reaction for the two reactions. Based on the provided heat capacities and formation enthalpies, we have \(\Delta H) for the first reaction equals to \(-65 - 2*(-242) +620 = 301\) kJ/mol, and for the second reaction equals to \(-372 - (-242) +620 = 490\) kJ/mol. Hence, the total heat added equals to \(x*\Delta H1 + y*\Delta H2 = 22.5*301 + 2.5*490 = 7987.5\) kJ/mol. Because the heat content of the reactor after the reaction is greater than before, it indicates that heat needs to be removed.

04

Economic Viability Evaluation

For biodiesel production to be economically viable, the cost of making biodiesel fuel has to be compared to the cost of producing petroleum diesel. Factors to consider include: costs of raw materials, conversion, labor, capital investment as well as income from the sale of glycerol, acrolein and hydroxyacetone. If the total cost of biodiesel production is less or the profit from these co-products can offset the extra cost, the process is economically viable.

05

Degree-of-Freedom Analysis Based on Atomic Species Balances

If the degree-of-freedom analysis was done based on atomic species balances, it's likely to yield one more equation than there are unknowns, making it seem as if the system has negative degree of freedom. However, the system is known to have zero degree of freedom from the extents of reaction approach. This discrepancy arises from the fact that the atomic species balances are not independent equations. It can be shown by expressing one of the atomic species balance equations as a linear combination of the others, proving it to be a dependent equation.

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Key Concepts

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

Transesterification Process

The transesterification process is the chemical reaction used to produce biodiesel from triglycerides. This is a common method involving the exchange of the organic group R' of an ester with another alcohol, typically methanol or ethanol.

• This process is catalyzed by acids or bases.
• Triglycerides in fats are converted into glycerol and fatty acid esters.
• These fatty acid esters are what we call biodiesel.

As the reaction progresses, every 9 kilograms of biodiesel produced will generate 1 kilogram of glycerol as a byproduct. This substantial production of glycerol is a key consideration in the economic viability of biodiesel, as finding markets or uses for these byproducts can greatly impact cost-effectiveness. The process has three main steps:

• The mixing of alcohol with a catalyst, usually a strong alkaline such as sodium hydroxide (NaOH) or potassium hydroxide (KOH).
• The addition of the triglyceride, leading to the formation of biodiesel and glycerol.
• The separation and purification of the biodiesel and byproduct glycerol.

Glycerol Byproduct

In the biodiesel production process, glycerol is a byproduct and is crucial for determining the process's economic viability. Its chemical formula is C₃H₈O₃. Glycerol is an important commodity with applications in multiple industries. However, with biodiesel's growth, the supply of glycerol has exceeded demand, making it essential to find new uses or markets for it. A proposed solution involves converting glycerol into more valuable chemicals through specific reactions. These conversions yield:

• Acrolein ( C₃H₄O) - used mainly as a precursor to other chemicals. This reaction also produces water.
• Hydroxyacetone (acetol) ( C₃H₆O₂) - used in various chemical applications, adding value to glycerol. This reaction also produces water.

Efficient utilization of glycerol leads to improved sustainability and profitability of biodiesel production. Thus, it is crucial to explore and harness these conversion technologies to enhance the economics of using glycerol effectively.

Chemical Reaction Stoichiometry

Chemical reaction stoichiometry involves balancing the reactants and products during a chemical process. This is critical when producing biodiesel through transesterification or converting glycerol into other chemicals.

• Stoichiometry helps us determine the amounts of reactants required and the expected yield of products.
• In the transesterification process, it's vital to know precisely how much alcohol and catalyst to add to convert all the triglycerides into biodiesel and glycerol.
• For glycerol conversion processes, stoichiometry allows us to predict how much acrolein and hydroxyacetone will be produced.

For the provided reactions in this process, you assume 100 mol is fed into the reactor, with glycerol fully consumed. The stoichiometric relations for glycerol's conversion equations give us insights into product distribution.
For instance: - From the glycerol conversion to acrolein and hydroxyacetone, the stoichiometry reveals a **9:1** production ratio between acrolein and hydroxyacetone. - This helps calculate the molar amounts of each resulting product, ensuring precise control in the manufacturing process.

Heat Capacity Calculations

By understanding heat capacity calculations, you can manage the energy requirements of biodiesel production and glycerol conversion processes effectively. Heat capacity is the amount of heat energy required to raise the temperature of a substance by one-degree Celsius.

• This property determines how energy-efficient a process is.
• It involves thermodynamic considerations to evaluate how much heat needs to be added or removed from a reaction system.

In the context of the exercise, let's break it down: - Using the given heat capacities for the species in the process (e.g., 0.1745 kJ/mol°C for glycerol vapor), you can calculate the total heat involved. - Combined with the enthalpy changes for the reactions, the calculations reveal that you add or remove energy depending on whether the reactor output contains more or less heat than the input. - For instance, the example shows the heat added calculation, indicating it’s necessary to remove excess heat, ensuring the reaction maintains desirable parameters.