1.1 Mass and Energy Balances

Mass and energy balances are fundamental principles in chemical engineering. They help us track materials and energy flowing through processes, ensuring nothing is created or destroyed. These concepts are crucial for designing and optimizing chemical systems.

Understanding mass and energy balances allows engineers to predict process behavior and efficiency. By applying conservation laws, we can solve problems involving steady-state and transient systems, considering various stream types like feed, product, waste, recycle, and purge streams.

Mass and Energy Balances

Mass conservation in chemical processes

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• Law of conservation of mass states that mass cannot be created or destroyed in a chemical process, meaning the total mass of inputs equals the total mass of outputs (reactants, products)
• Mass balance equations describe the flow of mass in a system: Accumulation = Input - Output + Generation - Consumption
  • In steady-state processes, accumulation is zero as the mass flow rates remain constant over time (continuous flow reactors)
• Reactive systems require considering stoichiometry and extent of reaction to account for changes in composition due to chemical reactions (combustion, synthesis)

Energy balances for systems

• Law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another (thermal, mechanical, electrical)
• Types of energy include:
  • Kinetic energy associated with motion: $KE = \frac{1}{2}mv^2$
  • Potential energy associated with position or configuration: $PE = mgz$
  • Internal energy dependent on temperature, pressure, and composition: $U = U(T, P, n)$
• Open systems involve mass flow across system boundaries, with the energy balance equation: $\Delta U = Q - W + \sum_{in} m_i h_i - \sum_{out} m_j h_j$
  • Consider flow work and enthalpy of incoming and outgoing streams (heat exchangers, turbines)
• Closed systems have no mass flow across system boundaries, simplifying the energy balance equation to: $\Delta U = Q - W$

Mass and energy balance problem-solving

• Steady-state problems involve zero accumulation terms, allowing for solving algebraic equations for unknown variables (flow rates, compositions)
• Transient problems have non-zero accumulation terms, requiring solving differential equations for time-dependent variables (batch reactors, start-up/shut-down)
• Problem-solving strategies:

1. Define system boundaries to identify inputs, outputs, and interactions with surroundings
2. Identify known and unknown variables based on given information and problem statement
3. Write and simplify balance equations by applying conservation laws and constitutive relations
4. Solve equations using appropriate techniques such as algebraic manipulation or integration (Excel, MATLAB)

Types of process streams

• Feed streams are input streams containing raw materials or reactants that contribute to mass and energy input terms (natural gas, crude oil)
• Product streams are output streams containing desired products that contribute to mass and energy output terms (gasoline, plastics)
• Waste streams are output streams containing undesired byproducts or waste materials that contribute to mass and energy output terms (flue gas, wastewater)
• Recycle streams are output streams that are partially or fully returned to the process, affecting mass and energy balance calculations by reducing net input or output (unreacted reagents, solvents)
• Purge streams are output streams used to remove accumulating inerts or impurities that contribute to mass and energy output terms (nitrogen, heavy metals)