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Lecture 9

Introduction to Material and Energy Balances (M.E.B.)

• Focus on key topics:

  • Process Flow Diagrams (PFD)

  • Block diagrams, streams, and units

  • Material balances on units

Degrees of Freedom (D.O.F.)

• Understanding degrees of freedom helps in defining the system variables and constraints.

• Referenced section: 3.4

Reactive Systems

• Key components of reactive systems:

  • Extent of reaction

  • Multiple reactions

  • Recycle processes

  • Yield and selectivity referenced in Section 4.3.4

PFD as Linear Systems

• Discussed in Section 3.3, emphasizing the linear representation of various systems in PFD.

Procedure for M.E.B. Analysis

• Steps to analyze a process:

  • Draw diagram: Create a detailed PFD labeling streams and units.

  • Define stream variables: Be specific and track variables associated with each stream.

  • Identify specifications: Write specifications in terms of the defined variables.

  • Perform D.O.F. analysis: Determine the best approach based on degrees of freedom.

  • Write out species balances: Essential for calculations and ensuring mass conservation.

  • Convert specifications into equations: Ensure that all variables correspond to defined stream properties.

  • Solve and analyze the system: Analyze solutions and outcomes to evaluate the process effectively.

Reactor Terminology and Concepts

• Extent of reaction: Measured as the change in moles of a reactant over time:

  • $f<em>{i} = rac{n</em>{i, ext{out}}}{n_{i, ext{in}}}$

  • This also encompasses the concept of conversion of species, represented mathematically.

• Conversion:

  • Definition: A measure of how much reactant is transformed into product.

  • It can be expressed in terms of moles or mass, and the concept is fundamental in reactor design.

• Reactor performance: High efficiency can be achieved even with low conversion rates.

Concepts of Conversion in Reactors

• Define multiple conversions:

  • Single pass conversion from initial to final state: $A<em>{2}$ to $A</em>{3}$

• Overall system conversion can differ based on behavior in the process flow.

Discussion Regarding Inerts

• Importance of managing inerts in chemical processes:

  • Inerts are substances that do not participate in the reaction.

  • Their presence is not conserved and complicates material balances, as they can dilute reactants, leading to lower concentrations and possibly affecting yield.

Fractional Conversion and Recycle

• Fraction recycled: Defined often in terms of the percentage of reactants recycled back into the system

  • $FR = rac{E<em>{ ext{recycled}}}{E</em>{ ext{out}}}$

• The importance of the flow rate of recycle is emphasized as it impacts overall reaction conversion significantly.

Impact of Reactant Ratios on Conversion

• When analyzing reactions, consider:

  • Excess and limiting reactants:

  • Example: In the reaction $2A + B <br>ightarrow 3C$, if A is in excess, $n<em>{A, ext{in}} > 2n</em>{B, ext{in}}$ is defined.

  • Excess reactant affects system performance compared to stoichiometric feed rates.

Multiple Reactions

• Tools for evaluating reactions:

  • Multiple reactions increase complexity; tools are needed to compare efficiencies and product yields.

• Example:

  • If reaction $R<em>1: 2A ightarrow B + W$ and $R</em>2: B <br>ightarrow C + W$ occur simultaneously, the yield must be defined carefully considering side reactions.

Definitions of Yield and Selectivity

• Yield: Ratio of moles of desired product formed to moles of reactant consumed.

  • $Y_{A <br>ightarrow P} = rac{ ext{mol of } A ext{ converted to product P}}{ ext{mol of } A ext{ fed}}$

• Selectivity: Ratio that represents the efficiency of the reaction towards the desired product versus undesired products:

  • $S_{A <br>ightarrow B} ext{ (for competing reactions)} = rac{ ext{mol of P generated from } A}{ ext{mol of A consumed}}$

Lecture 10

Continuing M.E.B. Concepts

• Key focus areas will include:

  • Process Flow Diagrams (PFD)

  • Introduction to equilibrium reactions in Section 5.1

Basic Reactor Functions

• A basic representation can be:

  • $A + B <br>ightarrow C + D$ (with solid catalysts as necessary for optimal performance)

  • Perfect reactor definitions where the reaction goes to completion.

  • Examples of stream variables will be supplied, emphasizing the systematic tracking of flows throughout the process.

Equilibrium in Reactive Systems

• Real reactions occur in both forward and reverse directions.

• The equilibrium constant can be expressed as:

  • $K_a = rac{[ ext{products}]}{[ ext{reactants}]}$

• Activity of species under equilibrium conditions plays a critical role in calculating the equilibrium constant.

  • Often relative to partial pressures for gases.

Examples of Equilibrium Constants

• Ammonia synthesis reaction:

  • $N<em>2 + 3H</em>2 <br>ightarrow 2NH_3$ and calculating the constant based on phases and conditions needed.

Summary of Key Takeaways

Definition and Calculation of Ka

• The relationship between Gibbs free energy change and the equilibrium constant:

  • $K_a = ext{exp}\biggl(- rac{ riangle G}{RT}\biggr)$

• Models are often evaluated at standard conditions.

  • The importance of considering temperature when determining equilibrium constants as it greatly affects reactive behavior.

Key Variables in Reactor Design

1. Reactor size and flow rates

2. Amounts and concentrations of reactants

3. Temperature, pressure, and their influence on reaction efficiency

4. Catalyst utilization and safety considerations

Conclusion and Next Steps

• Continue exploring comprehensive PFDs for complex systems.

• Welcome to the study of equilibrium reactions, including calculating how every variable plays into reactor design and efficiency in practical applications.