1.1 Fundamentals of Chemical Engineering Processes

Chemical processes rely on fundamental variables and units to describe and analyze systems. Mass, volume, temperature, pressure, and flow rate form the backbone of process calculations, allowing engineers to quantify and control material flows.

Understanding unit conversions and dimensional analysis is crucial for consistency in calculations. These skills enable engineers to work with diverse measurement systems and ensure accurate results when dealing with complex processes involving multiple units and streams.

Process Fundamentals and Units

Define and use process variables

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• Mass
  • Fundamental measure of amount of matter quantifies substance quantity
  • Measured in kilograms (kg) or pounds (lb) (1 kg = 2.2 lb)
• Volume
  • Space occupied by substance determines container size needed
  • Measured in cubic meters (m³) or liters (L) (1 m³ = 1000 L)
• Temperature
  • Average kinetic energy of particles indicates heat content
  • Common scales: Celsius (℃), Fahrenheit (℉), Kelvin (K) (0℃ = 32℉ = 273.15 K)
• Pressure
  • Force exerted per unit area affects fluid behavior
  • Measured in pascals (Pa) or atmospheres (atm) (1 atm = 101,325 Pa)
• Flow rate
  • Quantity of material passing through point per unit time crucial for process control
  • Mass flow rate: kg/s or lb/hr (1 kg/s = 7,936.64 lb/hr)
  • Volumetric flow rate: m³/s or L/min (1 m³/s = 60,000 L/min)
• Density
  • Mass per unit volume characterizes material properties
  • $\rho = \frac{m}{V}$
  • Units: kg/m³ or g/cm³ (1000 kg/m³ = 1 g/cm³)
• Concentration
  • Amount of solute per unit volume of solution determines mixture strength
  • Expressed as molarity (M), mass percent, or mole fraction (1 M = 1 mol/L)

Convert between different units of measurement

• SI prefixes
  • kilo- (k): 10³ multiplies by 1000
  • centi- (c): 10⁻² divides by 100
  • milli- (m): 10⁻³ divides by 1000
• Common conversions
  • Length: 1 inch = 2.54 cm used in pipe sizing
  • Mass: 1 lb = 453.592 g important for bulk material handling
  • Volume: 1 gallon = 3.78541 L crucial for tank design
• Dimensional analysis
  • Use conversion factors to cancel out units ensures consistency
  • Multiply by factors that equal 1 (100 cm / 1 m) simplifies complex conversions
• Temperature conversions
  • Celsius to Fahrenheit: $°F = (°C × \frac{9}{5}) + 32$ used in heat transfer calculations
  • Celsius to Kelvin: $K = °C + 273.15$ essential for thermodynamic equations
• Pressure conversions
  • 1 atm = 101,325 Pa = 760 mmHg critical for vacuum and high-pressure processes

Material Balances and Process Calculations

Perform material balance calculations for processes without chemical reactions

• Conservation of mass principle
  • Mass in = Mass out + Mass accumulated fundamental law of mass balance
• Steady-state assumption
  • No accumulation over time simplifies calculations
  • Mass in = Mass out applies to continuous processes
• Process flow diagram analysis
  • Identify system boundaries defines scope of balance
  • Label all streams with known information organizes data
• Basis selection
  • Choose convenient reference (100 kg of feed) simplifies calculations
• Single-unit operations
  • Mixing: $m_{total} = m_1 + m_2 + ... + m_n$ applies to blending processes
  • Separation: $m_{feed} = m_{product1} + m_{product2} + ... + m_{productn}$ used in distillation, filtration
• Multiple-unit processes
  • Solve material balances for each unit builds complex process understanding
  • Connect units using stream compositions ensures overall mass conservation

Calculate compositions of mixtures and solutions

• Mass fraction
  • $x_i = \frac{m_i}{m_{total}}$ represents component's mass contribution
  • Sum of all mass fractions equals 1 useful for checking calculations
• Mole fraction
  • $y_i = \frac{n_i}{n_{total}}$ represents component's molecular contribution
  • Sum of all mole fractions equals 1 important in gas-phase reactions
• Concentration in solution
  • Molarity: $M = \frac{moles\:of\:solute}{liters\:of\:solution}$ used in reaction kinetics
  • Mass percent: $\%\:m/m = \frac{mass\:of\:solute}{mass\:of\:solution} × 100\%$ common in industry
• Conversion between composition types
  • Mass fraction to mole fraction: $y_i = \frac{x_i / MW_i}{\sum (x_j / MW_j)}$ essential for gas laws
  • Mole fraction to mass fraction: $x_i = \frac{y_i × MW_i}{\sum (y_j × MW_j)}$ used in liquid mixtures

Use degrees of freedom analysis to determine if a process is solvable

• Degrees of freedom
  • Number of variables independently specified determines solution approach
  • $DOF = \text{number of variables} - \text{number of independent equations}$ guides problem-solving
• Solvability criteria
  • DOF = 0: Exactly solvable ideal case
  • DOF > 0: Underspecified requires additional information or assumptions
  • DOF < 0: Overspecified indicates redundant or conflicting data
• Equation types in material balances
  • Overall mass balance sums all inputs and outputs
  • Component mass balances track individual species
  • Summation equations (sum of mass fractions = 1) ensure completeness
• Strategy for solving material balances
  1. List all variables identifies unknowns
  2. Write all possible independent equations organizes problem
  3. Calculate DOF determines solvability
  4. If DOF = 0, solve system of equations yields solution