Mole balances

Chemical Reaction Engineering

Table of contents

• Introduction
• Mole balance

Introduction

• Chemical processes
• What is reaction engineering?
• Industrial reactors
• Overview of reaction engineering

Chemical processes

• Selection of reactor system is key to economic success or failure of a chemical plant

• Understanding how chemical reactors work lies at the heart of almost every chemical processing operation.

Typically, all chemical processes are designed to convert raw materials to produce a product that meet all the quality specifications and is ready for the market.

These chemical processes broadly involve three steps.

Initially, the raw materials are subjected to a sequence of physical treatments to refine them into a form suitable for chemical reaction. This may include the removal of impurities that could adversely affect the catalyst within the reactor.

These materials, once treated, are introduced into the reactor, which is the central component of the process. In this stage, the raw materials are chemically transformed, yielding a mixture of desired products along with by-products.

The reaction step typically does not yield pure products due to unreacted raw materials and the formation of by-products. Consequently, a separation step is essential after the reaction to isolate the desired products from the undesired ones.

Materials that do not react are returned to the beginning of the chemical process. This recycling is critical for efficient raw material utilization, ensuring the process remains economically viable.

The economic success of any chemical process is critically dependent on the design of the reactor. It requires a delicate balance – minimizing the costs associated with the reactor itself while also accounting for the expense involved in treating materials after the reaction has taken place.

Therefore, understanding how chemical reactors work lies at the heart of almost every chemical processing operation.

What is reaction engineering

• CRE is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place.

• Reactor design is a specialized task that involves evaluating various options. It draws on knowledge from thermodynamics, kinetics, fluid mechanics, and heat and mass transfer, along with economic considerations.

• CRE is the synthesis of all these factors with the aim of properly designing and understanding the chemical reactor.

It is the primary knowledge of chemical kinetics and reactor design that distinguishes the chemical engineer from other engineers

In unit operations, we focus on the design of equipment for the physical treatment steps. Whereas, chemical reaction engineering is concerned with the chemical treatment step of a process.

Chemical reaction engineering, or CRE, is dedicated to understanding the rates at which chemical reactions occur and the underlying mechanisms. CRE is also about the design of the reactors themselves, where these reactions take place.

The real challenge in CRE is to bring together knowledge from thermodynamics, chemical kinetics, and even economics. Our aim is to create reactors that are not just efficient at processing materials but also cost-effective. This balance is key to the economic feasibility of the entire chemical process.

So, CRE is about synthesis. It’s about combining all these complex factors to design a reactor that we fully understand and that operates optimally.

And it’s this specific knowledge in chemical kinetics and reactor design that really sets chemical engineers apart from other engineers. It’s our domain, where we apply our specialized skills to make a significant impact in the field of chemical processing.

Industrial reactors

Batch reactor

Batch reactors are used in pharmaceutical industry, and Specialty chemicals manufacturing. They are versatile and are used for operations where flexibility in operations is required.

Industrial reactors

Tubular reactor

Tubular reactors are typically used for continuous processing in chemical manufacturing. Its design allows for efficient heat and mass transfer, making it ideal for large-scale production.

Industrial reactors

Stirred reactor

Stirred reactors are commonly used in industrial applications for processes that require uniform mixing. Its design allows for consistent distribution of reactants and efficient reaction management.

Industrial reactors

Catalytic cracking reactor

This slide shows a catalytic cracking reactor, a key component in petroleum refineries. These reactors break down large hydrocarbon molecules into smaller, more valuable ones like gasoline and diesel. They are crucial for maximizing the yield of high-demand fuels from crude oil.

Industrial reactors

Calcination kiln

This is an image of a calcination kiln, an industrial reactor used to process raw materials at high temperatures. This type of kiln is integral to the production of cement, lime, and various other materials that require high-temperature treatment to alter their physical or chemical properties before further processing.

Industrial reactors

Microreactors

Microreactors are small-scale continuous flow reactors that allow precise control of reaction conditions. They’re used for rapid testing of chemical reactions and process optimization, and are becoming increasingly important in pharmaceuticals, fine chemicals, and research and development due to their efficiency and scalability.

Industrial reactors

Electrolyzers

Industrial electrolyzers are specialized reactors used for electrochemical processes such as hydrogen production via water electrolysis.

Industrial reactors

Raceway ponds

Raceway ponds are open-air shallow ponds used in the cultivation of algae and other aquatic organisms. They are often used in the biofuel industry for growing algae that can be converted into biodiesel. These systems allow for controlled conditions to optimize the growth rate of the algae and are an example of bioreactors in industrial biotechnology.

How do we design a chemical reactor?

To evaluate a reactor’s performance, we need to establish a performance equation. This mathematical relationship correlates the inputs like concentrations, flow rates, and temperatures to outputs including product concentration, temperature, and conversion. This equation is crucial for comparing different reactor designs and operational conditions, optimizing performance, and scaling up from laboratory to industrial scale.

Understanding the contacting pattern is also essential. This refers to the manner in which materials move and interact within the reactor, including the timing of their mixing and their physical characteristics such as clumpiness or dispersal. For instance, some materials naturally form clumps, like solids, or may not easily mix, like certain noncoalescing liquids.

Kinetics, the study of reaction rates, is a fundamental aspect of reaction engineering. If reactions occur quickly, equilibrium conditions will largely dictate the reactor’s output. For slower reactions, the reaction rate, alongside heat and mass transfer rates, become significant factors in determining the reactor’s performance. These principles allow chemical engineers to design reactors that meet specific process requirements.

How do we design a chemical reactor?

Maximize the space-time yield

Reaction

• Stoichiometry
• Kinetics: elementary vs non-elementary
• Single vs multiple reactions

Reactor

• Isothermal vs non-isothermal
• Ideal vs nonideal
• Steady-state vs nonsteady-state

Raceway ponds are open-air shallow ponds used in the cultivation of algae and other aquatic organisms. They are often used in the biofuel industry for growing algae that can be converted into biodiesel. These systems allow for controlled conditions to optimize the growth rate of the algae and are an example of bioreactors in industrial biotechnology.

Mole balance

• Rate of reaction

• Basic mole balance

• Mole balance in reactors

  • Batch reactor
  • Continuous stirred tank reactor (CSTR)
  • Plug flow reactor (PFR)
  • Packed bed reactor (PBR)

Reaction rate

• A chemical species is said to have reacted when it has lost its chemical identity.

• The identity of a chemical species is determined by the kind, number, and configuration of that species’ atoms.

• There are three ways for a species to loose its identity:

  • Decomposition: \ce{CH3-CH3 -> H2 + H2C=CH2}

  • Combination: \ce{N2 + O2 -> 2NO}

  • Isomerization: \ce{C2H5CH=CH2 -> CH2=C(CH3)2}

• The rate of reaction tells us how fast a number of moles of one chemical species are being consumed to form another chemical species.

• The rate of a reaction (mol/dm^3/s) can be expressed as either:

  • The rate of Disappearance of reactant: -r_A
  • The rate of Formation (Generation) of product: r_P

Some reactions occur very rapidly; others very, very slowly. For example, in the production of polyethylene, one of our most important plastics,or in the production of gasoline from crude petroleum, we want the reaction step to be complete in less than one second, while in waste water treatment, reaction may take days and days to do the job.

Reaction rate

\ce{A + B -> C + D}

• r_A, r_B = the rate of formation of species A, and B per unit volume
• -r_A, -r_B = the rate of a disappearance of species A, and B per unit volume

• r_C, r_D = the rate of formation of species C, and D per unit volume

• For species j:
  • r_j is the rate of formation of species j per unit volume [e.g. mol/dm^3 s]
  • r_j is a function of concentration, temperature, pressure, and the type of catalyst (if any)
    
  • r_j is independent of the type of reaction system (batch, plug flow, etc.)
  • r_j is an algebraic equation, not a differential equation

The algebraic expression for the reaction rate equation, r_j, is also known as the rate law.

Rate law

-r_A = f \begin{bmatrix} \text{temperature dependent terms}, & \text{concentration dependent terms} \end{bmatrix}

• Some examples of rate law

  • Arrhenius equation: -r_A = A e^{-E_A/RT} C_A^a

    • A: Pre-exponential factor
    • E_A: Activation energy
    • R: Gas constant
    • T: Temperature
    • C_A: concentration
    • a: order of the reaction

  • Michaelis-Menton kinetics: -r_A = \frac{k_1 C_A}{1 + k_2 C_A}

• For a catalytic reaction we refer to –r_A’ , which is the rate of disappearance of species A on a per mass of catalyst basis. (mol/gcat/s).

General mole balance

\text{in} - \text{out} + \text{generation} = \text{accumulation}

\begin{array}{c} \text {rate of} \\ \text {flow of } j \\ \text {into system} \end{array} - \begin{array}{c} \text {rate of} \\ \text {flow of } j \\ \text {out of system} \end{array} + \underbrace{ \begin{array}{c} \text {rate of} \\ \text {generation} \\ \text {of } j \text { by rxn} \end{array} - \begin{array}{c} \text {rate of} \\ \text {decomposition} \\ \text {of } j \text { by rxn} \end{array} }= \begin{array}{c} \text {rate of} \\ \text {accumulation} \\ \text {of } j \end{array}

F_{j0} \qquad - \qquad F_j \qquad + \qquad G_j \qquad = \qquad \frac{dN_j}{dt}

\frac{mol}{s} \qquad + \qquad \frac{mol}{s} \qquad + \qquad \frac{mol}{s} \qquad = \qquad \frac{d}{dt}\left(mol\right)

Uniform generation

G_j = r_j V

\left[ \begin{array}{c} \text {moles of } j \\ \text {generated per} \\ \text {unit time} (mol/s) \end{array} \right] = \left[ \begin{array}{c} \text {moles of } j \\ \text {generated per} \\ \text {unit time and} \\ \text {volume }(mol/s \cdot m^3) \end{array} \right] \left[ \begin{array}{c} \text {} \\ \text {Volume} \\ (m^3) \\ \text {} \end{array} \right]

F_{j0} \qquad - \qquad F_j \qquad + \qquad r_j V \qquad = \qquad \frac{dN_j}{dt}

Non-uniform generation

G_j = \sum_{i=1}^{n} r_{ji} \Delta V_i

G_j=\lim _{\substack{n \rightarrow \infty \\ \Delta V \rightarrow 0}} \sum_{i=1}^n r_j \Delta V = \int^V r_j d V

F_{j0} \qquad - \qquad F_j \qquad + \qquad \int^V r_j dV \qquad = \qquad \frac{dN_j}{dt}

Review - general mole balance

• General form: F_{j0} - F_j + G_j = \frac{dN_j}{dt}

• Uniform generation F_{j0} - F_j + r_j V = \frac{dN_j}{dt}

• Non-uniform generation F_{j0} - F_j + \int^V r_j dV = \frac{dN_j}{dt}

Batch reactor

• Reactants placed in reactor (Charge); reaction allowed to proceed over time.

• Closed system: no reactants added or products removed during reaction.

• Unsteady-state: composition changes over time.

• Ideal batch reactor: contents perfectly mixed.

• Concentration and temperature are uniform throughout the reactor but change with time.

• Typical uses: Small scale operations, expensive products (e.g. pharmaceutical), new processes.

Continuous stirred tank reactor (CSTR)

• Open system: Reactants are continuously fed and products removed.
• The incoming stream blends immediately with the reactor’s contents.
• Perfect mixing: similar to an ideal batch reactor.
• Temperature and concentration are consistent throughout.
• Exit stream composition matches the reactor’s interior.
• Reaction rates are constant, maintaining steady-state.

• Typical uses: Large-scale industrial chemical production (e.g. metallurgy), wastewater treatment

Plug flow reactor (PFR)

• Also known as a tubular reactor.
• Cylindrical shape with openings at both ends.
• Materials move steadily through the reactor’s length.
• Reactants are consumed along the reactor’s length.
• Steady state operations:
  • No radial gradients Temperature, concentration, reaction rates are constant at any given cross section.
  • All material spends exactly same time in the reactor.

• Typical examples: Food industry (continuous baking or sterilization), polymerization reactions

Packed bed reactor (PBR)

• Vertical cylindrical shell design.

• Flow is often gravity-driven.

• Heterogeneous reactions with a fixed catalyst bed.

• Reactants pass from top through the catalyst layer.

• Concentration gradient forms along the reactor’s length.

• Reactions occur at catalyst pellet surfaces.

• Reaction rate (r'_A)depends on catalyst mass (W), not reactor volume (V).

• Typical examples: Catalytic converters, petroleum refining, air purification

Selection of reactors

• Batch
  • small scale, production of expensive products (e.g. pharmacy)
  • high labor costs per batch
  • difficult for large-scale production
• CSTR: most homogeneous liquid-phase flow reactors
  • when intense agitation is required
  • relatively easy to maintain good temperature control
  • the conversion of reactant per volume of reactor is the smallest of the flow reactors - very large reactors are necessary to obtain high conversions
• PFR: most homogeneous gas-phase flow reactors
  • relatively easy to maintain
  • usually produces the highest conversion per reactor volume (weight of catalyst if it is a packed-bed catalyze gas reaction) of any of the flow reactors
  • difficult to control temperature within the reactor
  • hot spots can occur

Mole balance: Batch reactor

Assumptions

1. Perfect mixing: The reactor contents are perfectly mixed (Ideal reactor).
2. Constant Volume: The reactor volume is constant.
3. Constant Physical Properties: The physical properties (density, viscosity, etc.) of the reaction mixture are constant.
4. Single Reaction Phase: The reaction is assumed to occur in a single phase (either all gas, all liquid, or all solid).
5. Closed system: No material is lost to the surroundings.

Mole balance: Batch reactor

Mole balance: CSTR

Assumptions

1. Steady-State Operation: No accumulation of reactants or products over time.
2. Continuous Flow: Material continuously flows into and out of the reactor.
3. Perfect mixing: The composition is uniform throughout the reactor.
4. Constant Volume: The volume of fluid within reactor remains constant.
5. Constant Physical Properties

Mole balance: CSTR

Mole balance: PFR

Assumptions

1. Steady-State Operation: no accumulation of materials in any section of the reactor over time.
2. Plug Flow: The flow through the reactor is plug flow, meaning all elements of the fluid move with the same velocity and there’s no back-mixing.
3. Constant Cross-Sectional Area: The cross-sectional area of the PFR is constant along its length.
4. One-Dimensional Flow: The flow of reactants and products is considered only in the axial direction, ignoring effects in the radial or circumferential directions. Concentration and temperature changes along the length of the reactor not radially.
5. No pressure drop; Constant Physical Properties

Mole balance: PFR

Mole balance: PBR

Assumptions

1. Steady-State Operation
2. One-Dimensional Flow
3. No pressure drop; Constant Physical Properties
4. No Back-Mixing: The reactor operates under plug flow conditions with no back-mixing or axial dispersion of reactants or products.
5. Constant Cross-Sectional Area: The cross-sectional area of the PFR is constant along its length.
6. Uniform Packing: Constant surface area for reaction per unit reactor volume.

Mole balance: PBR