3.1 Conservation of mass

Material balances are the backbone of chemical engineering. They help us track mass flow through systems, ensuring nothing is created or destroyed. By applying conservation of mass, we can analyze and optimize processes, from reactors to entire plants.

Understanding system boundaries is key to solving material balance problems. By defining what's included, we can focus on relevant inputs and outputs. This approach simplifies complex processes and guides us in designing efficient, environmentally-friendly systems.

Conservation of Mass in Chemical Engineering

The Law of Conservation of Mass

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• The law of conservation of mass states that matter cannot be created or destroyed in an isolated system, only transformed from one form to another
• In a chemical reaction, the total mass of reactants must equal the total mass of products, as atoms are conserved (reactants → products)
• The law of conservation of mass is a fundamental principle in chemical engineering, as it forms the basis for material balances and process design
• Chemical engineers use the law of conservation of mass to analyze and optimize chemical processes, ensuring that the desired products are obtained while minimizing waste and environmental impact (wastewater treatment, biofuel production)

Applications in Chemical Engineering

• Material balances: The law of conservation of mass is applied to determine the flow rates, compositions, and quantities of materials entering and leaving a system
• Process design: Chemical engineers use the law of conservation of mass to design and size equipment, such as reactors, separators, and heat exchangers (distillation columns, absorption towers)
• Optimization: By applying the law of conservation of mass, chemical engineers can identify opportunities to improve process efficiency, reduce waste, and minimize raw material consumption (recycling streams, heat integration)
• Environmental impact assessment: The law of conservation of mass helps chemical engineers quantify the environmental impact of a process by tracking the fate of pollutants and byproducts (greenhouse gas emissions, wastewater discharge)

System Boundaries for Material Balances

Defining System Boundaries

• A system boundary is an imaginary surface that separates the system under study from its surroundings, defining what is included in the material balance analysis
• The system boundary can be drawn around a single piece of equipment, a group of equipment, or an entire process, depending on the scope of the analysis (reactor, distillation column, chemical plant)
• The choice of system boundary determines which streams of matter and energy cross the boundary and must be accounted for in the material balance
• A well-defined system boundary is crucial for accurately applying the law of conservation of mass and solving material balance problems
• The system boundary concept allows chemical engineers to simplify complex processes and focus on the relevant inputs, outputs, and transformations within the system

Types of System Boundaries

• Open systems: Matter and energy can cross the system boundary (continuous stirred-tank reactor, heat exchanger)
• Closed systems: Only energy can cross the system boundary, while matter is conserved within the system (batch reactor, pressure vessel)
• Isolated systems: Neither matter nor energy can cross the system boundary (adiabatic reactor, insulated storage tank)
• Steady-state systems: The system operates at constant conditions, with no accumulation or depletion of mass or energy within the system boundaries (continuous distillation column, pipeline)
• Unsteady-state systems: The system conditions change with time, and accumulation or depletion of mass or energy occurs within the system boundaries (batch reactor, start-up or shutdown of a process)

Solving Steady-State Material Balances

The Steady-State Material Balance Equation

• Steady-state material balances assume that the system is operating at constant conditions, with no accumulation or depletion of mass within the system boundaries
• The general steady-state material balance equation is: Input = Output + Consumption - Generation, where consumption and generation refer to chemical reactions or phase changes within the system
• To solve steady-state material balance problems:
  1. Identify the system boundary
  2. List all streams crossing the boundary
  3. Apply the conservation of mass equation for each component or overall mass
• When dealing with multiple components, it is often necessary to combine the component balances with additional equations, such as reaction stoichiometry or phase equilibrium relationships (ideal gas law, Raoult's law)
• Solving steady-state material balance problems enables chemical engineers to determine stream flow rates, compositions, and other process variables required for equipment sizing and process optimization

Problem-Solving Strategies

• Develop a systematic approach to solving material balance problems:
  1. Read the problem statement carefully and identify the given information and the required solution
  2. Draw a process flow diagram with a clearly defined system boundary and labeled streams
  3. Write the relevant material balance equations for each component and the total mass
  4. Combine the balance equations with additional equations or relationships, if necessary
  5. Solve the equations simultaneously to determine the unknown variables
• Use appropriate units and convert them consistently throughout the problem (SI units, English units)
• Check the reasonableness of the results by comparing them with typical values or expected ranges (order-of-magnitude estimates, industry benchmarks)
• Perform a degrees-of-freedom analysis to ensure that the problem is solvable with the given information (number of independent equations = number of unknown variables)

Extensive vs Intensive Properties in Material Balances

Defining Extensive and Intensive Properties

• Extensive properties are those that depend on the amount of matter in the system, such as mass, volume, and energy. They are additive for subsystems (total mass = sum of component masses)
• Intensive properties are independent of the amount of matter in the system and represent the quality or state of the system, such as temperature, pressure, and concentration (boiling point, pH)
• In material balances, extensive properties are conserved and can be balanced directly using the law of conservation of mass
• Intensive properties are not conserved but can be used to relate the properties of different streams or to determine the state of the system

Using Extensive and Intensive Properties in Material Balances

• When solving material balance problems, it is essential to correctly identify and use extensive and intensive properties to ensure the accuracy of the results and the validity of the assumptions made
• Extensive properties are used in the conservation equations, such as mass balances for individual components or total mass (component flow rates, total mass flow rate)
• Intensive properties are used to relate the properties of different streams or to determine the state of the system, such as using temperature and pressure to calculate the density or enthalpy of a stream (ideal gas law, steam tables)
• Intensive properties can be used to convert between extensive properties, such as using density to convert mass to volume or vice versa ($\rho = m/V$)
• When combining streams, extensive properties are additive, while intensive properties may require weighted averages based on the relative amounts of the streams (mixing of hot and cold streams, blending of different concentrations)