Chemical & Process Engineering

📘 Key Concepts and Definitions

• Mass Balance: An application of conservation of mass to the analysis of physical systems. It states that mass cannot be created or destroyed.
• Energy Balance: An application of the first law of thermodynamics, stating that energy cannot be created or destroyed.
• Distillation: A process of separating the components of a liquid mixture by using selective boiling and condensation.
• Reaction Kinetics: The study of chemical reaction rates and the factors that affect them.
• Flammability Limits (LEL/UEL): The concentration range of a gas or vapor in air that can ignite. LEL = Lower Explosive Limit, UEL = Upper Explosive Limit.

🧮 Formulas and Equations

Mass & Energy Balances

• General Balance Equation: Accumulation = In - Out + Generation - Consumption
• Steady-State Mass Balance: Σṁ_in = Σṁ_out
• Steady-State Energy Balance (no reaction): Σ_in(ṁ_iĤ_i) - Σ_out(ṁ_jĤ_j) + Q̇ - Ẇ_s = 0
• Where ṁ is mass flow rate, Ĥ is specific enthalpy, Q̇ is heat transfer, and Ẇ_s is shaft work.

Reaction Kinetics

• Rate Law (n-th order): -r_A = kC_Aⁿ
• Arrhenius Equation: k = A e^{-Ea / RT}
• Where -r_A=rate of reaction, k=rate constant, C_A=concentration of A, n=reaction order, A=pre-exponential factor, E_a=activation energy, R=ideal gas constant, T=absolute temperature.

Fluid Flow in Pipes

• Pressure Drop (Darcy-Weisbach): ΔP = f (L/D) (ρV²/2)
• This is a rearrangement of the head loss equation from fluid mechanics, expressed in terms of pressure. The friction factor f is typically found using a Moody Chart.

🛠️ Tools & Methods

McCabe-Thiele Method

A graphical method for determining the theoretical number of stages required for a binary distillation column.

1. Plot the equilibrium curve (y vs. x).
2. Draw the q-line based on the feed condition (liquid, vapor, or mix).
3. Draw the upper and lower operating lines based on reflux ratio and bottoms composition.
4. Starting from the desired distillate composition, step down between the operating lines and the equilibrium curve until the bottoms composition is reached. Each step represents a theoretical stage.

🧭 Step-by-Step Guides: Relief Valve Sizing

A simplified workflow for sizing a relief valve for a gas or vapor.

1. Identify Overpressure Scenario: Determine the worst-case cause of overpressure (e.g., blocked outlet, external fire, thermal expansion).
2. Determine Required Relief Rate: Calculate the mass flow rate (ṁ) that must be vented to prevent pressure from exceeding the limit.
3. Calculate Required Orifice Area (A): Use a standard formula, such as the API 520 equation for gas/vapor relief. This formula depends on flow rate, pressure, temperature, molecular weight, and gas properties.
4. Select Standard Orifice Size: Choose the next largest standard orifice size (e.g., D, E, F, G...) that provides an area greater than or equal to the calculated required area.
5. Verify Inlet/Outlet Piping: Ensure the pressure drop in the piping to and from the valve does not compromise its performance.

⌨️ Productivity Tips

• Heat Capacity Estimation: For quick estimates, use constant heat capacities (C_p) for liquids and ideal gases if the temperature change is not large. For more accuracy, use correlations like C_p = A + BT + CT² + DT³.
• Friction Factor: For fully turbulent flow in smooth pipes, the friction factor is primarily a function of the Reynolds number. For rough pipes, it becomes nearly constant and depends only on relative roughness.

📊 Tables & Visual Aids

Flammability Diagram (Triangle)

A triangular graph that shows the flammability region of a mixture of fuel, oxidant (usually air), and an inert gas. It is a critical tool for process safety analysis, especially for inerting processes.

🧪 Use Case: Arrhenius Equation Example

Problem: A reaction has a rate constant k₁ = 0.05 s^-1 at T₁ = 300K. The activation energy is E_a = 40 kJ/mol. Find the rate constant k₂ at T₂ = 320K.

• Use the two-point form of the Arrhenius equation: ln(k₂/k₁) = -(E_a/R)(1/T₂ - 1/T₁)
• R = 8.314 J/(mol · K).
• ln(k₂/0.05) = -(40000/8.314)(1/320 - 1/300) = 1.0016.
• k₂/0.05 = e^1.0016 ≈ 2.72.
• k₂ ≈ 2.72 · 0.05 ≈ 0.136 s^-1.

🧹 Troubleshooting Common Issues

• Problem: Mass balance does not close.
  • Fix: Check for missing streams (leaks, vents), incorrect flow measurements, or unaccounted-for reactions (generation/consumption). Ensure all units are consistent.
• Problem: Distillation column is not achieving separation.
  • Fix: The reflux ratio may be too low, or the number of actual stages is insufficient. Physical issues like foaming, weeping, or flooding can also severely reduce tray efficiency.

📚 References and Further Reading

• Perry's Chemical Engineers' Handbook.
• "Elementary Principles of Chemical Processes" by Felder, Rousseau, and Bullard.
• "Elements of Chemical Reaction Engineering" by Fogler.
• "Unit Operations of Chemical Engineering" by McCabe, Smith, and Harriott.
• API Standards 520/521 for pressure relief systems.