🪫Chemical Process Balances Unit 10 – Energy Balance in Chemical Processes

Key Concepts and Definitions

• Energy balance fundamental principle in chemical engineering used to analyze and design chemical processes
• Thermodynamics branch of physics that deals with heat, work, and energy and their interactions
• System defined region or space where energy transfer and conversion occur
• Surroundings everything outside the system that can interact with it
• Internal energy (U) total energy contained within a system, including kinetic and potential energy of molecules
• Enthalpy (H) measure of the total heat content of a system at constant pressure
  • Defined as $H = U + PV$, where P is pressure and V is volume
• Heat (Q) transfer of thermal energy between systems or between a system and its surroundings
• Work (W) energy transfer that occurs when a force acts through a distance

Energy Forms in Chemical Processes

• Kinetic energy energy associated with the motion of an object or particles within a system
• Potential energy energy stored within a system due to its position or configuration
  • Includes gravitational potential energy and chemical potential energy
• Thermal energy internal energy associated with the random motion of particles within a system
• Chemical energy potential energy stored within the chemical bonds of molecules
• Electrical energy energy associated with the flow of electric charges (electrons)
• Radiant energy energy transmitted through space in the form of electromagnetic waves (light)
• Nuclear energy energy released during nuclear reactions (fission or fusion)

First Law of Thermodynamics

• Energy cannot be created or destroyed, only converted from one form to another
• Mathematical expression: $\Delta U = Q - W$
  • Change in internal energy ($\Delta U$) equals heat added to the system (Q) minus work done by the system (W)
• Applies to all systems, including chemical processes and reactions
• Provides a framework for analyzing energy changes and balances in chemical systems
• Helps determine the energy requirements or outputs of a process
• Enables the design of efficient and sustainable chemical processes
• Allows for the calculation of heat and work exchanges between a system and its surroundings

Energy Balance Equations

• Mathematical expressions that describe the conservation of energy within a system
• General energy balance equation: $\Delta U = Q - W + \sum m_i h_i - \sum m_e h_e$
  • $\Delta U$ change in internal energy
  • Q heat added to the system
  • W work done by the system
  • $m_i$ mass flow rate of inlet streams
  • $h_i$ specific enthalpy of inlet streams
  • $m_e$ mass flow rate of exit streams
  • $h_e$ specific enthalpy of exit streams
• Simplified energy balance equation for a steady-state process: $Q - W + \sum m_i h_i - \sum m_e h_e = 0$
• Energy balance equations can be modified to account for specific process conditions (adiabatic, isothermal, etc.)

Closed vs. Open Systems

• Closed systems have fixed boundaries and do not exchange mass with their surroundings
  • Energy can be exchanged as heat or work
  • Examples: batch reactors, pressure vessels, and sealed containers
• Open systems have permeable boundaries and can exchange both mass and energy with their surroundings
  • Mass enters and exits the system through inlet and outlet streams
  • Energy is exchanged as heat, work, and through the flow of mass
  • Examples: continuous reactors, heat exchangers, and distillation columns
• Energy balance equations differ for closed and open systems
  • Closed systems: $\Delta U = Q - W$
  • Open systems: $\Delta U = Q - W + \sum m_i h_i - \sum m_e h_e$

Heat Capacity and Enthalpy

• Heat capacity (C) measure of the amount of heat required to raise the temperature of a substance by one degree
  • Specific heat capacity (c) heat capacity per unit mass, $c = \frac{C}{m}$
• Enthalpy (H) measure of the total heat content of a system at constant pressure
  • Change in enthalpy $(\Delta H)$ equals the heat absorbed or released by a system during a process at constant pressure
• Relationship between heat capacity and enthalpy: $\Delta H = m \cdot c \cdot \Delta T$
  • m mass of the substance
  • c specific heat capacity
  • $\Delta T$ change in temperature
• Enthalpy of formation $(\Delta H_f)$ change in enthalpy when one mole of a compound is formed from its constituent elements in their standard states
• Hess's Law states that the total enthalpy change for a reaction is independent of the pathway or intermediate steps

Energy Balance Calculations

• Involve applying the energy balance equations to specific chemical processes or systems
• Require knowledge of the system boundaries, inlet and outlet streams, and process conditions
• Steps in solving energy balance problems:
  1. Define the system and its boundaries
  2. Identify the inlet and outlet streams and their properties (temperature, pressure, composition)
  3. Determine the process conditions (adiabatic, isothermal, steady-state, etc.)
  4. Select the appropriate energy balance equation based on the system type (closed or open)
  5. Substitute known values into the equation and solve for the unknown variable
• May involve the use of thermodynamic data (heat capacities, enthalpies of formation) and steam tables
• Can be used to determine the energy requirements (heating or cooling) for a process
• Help optimize process conditions to minimize energy consumption and costs

Real-World Applications

• Design and optimization of chemical reactors (batch, continuous, and semi-batch)
  • Determining heating or cooling requirements to maintain desired reaction conditions
• Heat exchanger design and analysis
  • Calculating the heat transfer rate and the required surface area for a given temperature change
• Distillation column energy requirements
  • Estimating the reboiler and condenser duties based on the feed composition and desired product purities
• Power generation in combustion processes
  • Analyzing the energy released during fuel combustion and the efficiency of the power generation cycle
• Refrigeration and air conditioning systems
  • Determining the work input required to achieve a desired cooling effect
• Energy audits and conservation in chemical plants
  • Identifying areas of energy waste and implementing strategies to reduce energy consumption
• Sustainable process design
  • Incorporating renewable energy sources and minimizing the environmental impact of chemical processes