🪫Chemical Process Balances Unit 11 – Energy Balance in Steady-State Systems

Key Concepts and Definitions

• Energy the capacity to do work or transfer heat
• Thermodynamics the study of energy and its transformations
• Heat transfer of energy due to a temperature difference
• Work transfer of energy due to a force acting over a distance
• Internal energy the sum of the kinetic and potential energies of the particles in a system
• Enthalpy a thermodynamic property defined as $H = U + PV$, where $U$ is internal energy, $P$ is pressure, and $V$ is volume
  • Represents the total heat content of a system
• Steady-state a condition in which the properties of a system do not change with time
• Control volume a fixed region in space through which matter and energy can flow

Energy Forms and Conversions

• Kinetic energy the energy associated with the motion of an object $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity
• Potential energy the energy associated with the position or configuration of an object (gravitational, elastic)
• Chemical energy the energy stored in the bonds of chemical compounds
  • Released or absorbed during chemical reactions
• Electrical energy the energy associated with the flow of electric charges
• Thermal energy the energy associated with the random motion of particles in a substance
• Mechanical energy the sum of kinetic and potential energies in a system
• Energy conversion the process of changing energy from one form to another (chemical to thermal in combustion)

First Law of Thermodynamics

• States that energy cannot be created or destroyed, only converted from one form to another
• Mathematically expressed as $\Delta U = Q - W$, where $\Delta U$ is the change in internal energy, $Q$ is heat added to the system, and $W$ is work done by the system
• Applies to all forms of energy and all types of systems
• Provides a framework for analyzing energy balances in chemical processes
  • Helps determine the energy requirements and efficiencies of processes
• Implies that the total energy of an isolated system remains constant
• Allows for the calculation of heat and work interactions between a system and its surroundings

Energy Balance Equations

• Based on the first law of thermodynamics and the conservation of energy principle
• General steady-state energy balance equation: $\dot{Q} + \dot{W} = \Delta \dot{H} + \Delta \dot{KE} + \Delta \dot{PE}$
  • $\dot{Q}$ is the net rate of heat transfer
  • $\dot{W}$ is the net rate of work
  • $\Delta \dot{H}$ is the change in enthalpy flow rate
  • $\Delta \dot{KE}$ is the change in kinetic energy flow rate
  • $\Delta \dot{PE}$ is the change in potential energy flow rate
• Simplified for most steady-state processes: $\dot{Q} + \dot{W} = \Delta \dot{H}$
• Enthalpy change calculated using $\Delta \dot{H} = \dot{m}c_p\Delta T$, where $\dot{m}$ is mass flow rate, $c_p$ is specific heat capacity, and $\Delta T$ is temperature change

System Boundaries and Classifications

• System a specific region or object of interest for energy analysis
• Surroundings everything outside the system
• Open system can exchange both matter and energy with its surroundings
• Closed system can exchange energy but not matter with its surroundings
• Isolated system cannot exchange either matter or energy with its surroundings
• Control surface the boundary between the system and its surroundings
  • Can be real (pipe wall) or imaginary (a plane in space)
• Choice of system boundaries affects the complexity of energy balance calculations
  • Larger systems may simplify calculations by eliminating internal energy transfers

Steady-State Energy Calculations

• Involve applying the steady-state energy balance equation to a specific system
• Require identifying the system boundaries and all energy flows across them
• Assume that the properties of the system do not change with time
  • Mass flow rates, temperatures, pressures remain constant
• Often involve solving for an unknown variable (heat duty, temperature change, work)
• May require using thermodynamic properties (enthalpy, specific heat) and process data (flow rates, compositions)
• Can be simplified by neglecting small or insignificant energy terms (potential, kinetic)

Common Energy Balance Problems

• Heat exchanger calculations determining the heat duty or outlet temperatures
• Reactor energy balances accounting for heat of reaction and heat transfer
• Turbine and compressor work calculating power output or requirements
• Pump and valve energy balances considering changes in pressure and enthalpy
• Mixing and separation processes evaluating the energy effects of combining or separating streams
• Combustion processes analyzing the energy released from burning fuels
• Heating and cooling operations determining the energy needed to change the temperature of a process stream

Real-World Applications

• Design and optimization of heat exchanger networks in chemical plants
• Energy efficiency analysis of industrial processes (distillation, refrigeration)
• Sizing and selection of process equipment (reactors, pumps, compressors)
• Evaluation of alternative energy sources and technologies (solar, biomass)
• Pinch analysis for minimizing energy consumption and waste
• Cogeneration systems producing both heat and power from a single fuel source
• Energy audits and management in manufacturing facilities
• Sustainable design of buildings and HVAC systems