Ultimate Chemical Engineering Cheatsheet: Formulas, Processes & Calculations

Introduction to Chemical Engineering

Chemical engineering is the branch of engineering that applies physical sciences (physics and chemistry), life sciences (microbiology and biochemistry), together with mathematics and economics to produce, transform, transport, and properly use chemicals, materials and energy. It combines the knowledge of chemistry, physics, biology, and mathematics to solve problems related to the production or use of chemicals on an industrial scale.

Fundamental Concepts & Units

SI Units and Conversions

Dimensional Analysis

Step-by-step process:

1. Identify known quantities and target units
2. Write conversion factors as fractions
3. Multiply by conversion factors so units cancel
4. Calculate final value

Example: Convert 55 mph to m/s 55 (miles/hour) × (1609 m/mile) × (1 hour/3600 s) = 24.7 m/s

Thermodynamics

Laws of Thermodynamics

1. First Law (Conservation of Energy): Energy can neither be created nor destroyed, only transferred or converted

   • ΔU = Q – W
   • ΔU = change in internal energy
   • Q = heat added to system
   • W = work done by system

2. Second Law: The entropy of an isolated system always increases

   • ΔS ≥ 0 (for isolated systems)
   • ΔS = Q/T (for reversible processes)

3. Third Law: As temperature approaches absolute zero, entropy approaches a minimum value

Thermodynamic Properties

Enthalpy (H)

• H = U + PV
• ΔH = ΔU + Δ(PV)
• For constant pressure: ΔH = Q_p

Entropy (S)

• dS = δQ_rev/T
• ΔS = ∫(δQ_rev/T)
• For ideal gas: ΔS = C_p·ln(T₂/T₁) – R·ln(P₂/P₁)

Gibbs Free Energy (G)

• G = H – TS
• ΔG = ΔH – TΔS
• At equilibrium: ΔG = 0
• For spontaneous reaction: ΔG < 0

Equations of State

Ideal Gas Law

• PV = nRT
• P = pressure (Pa)
• V = volume (m³)
• n = moles
• R = gas constant (8.314 J/mol·K)
• T = temperature (K)

Van der Waals Equation

• (P + a(n/V)²)(V-nb) = nRT
• a = attractive parameter
• b = volume parameter

Virial Equation

• PV/nRT = 1 + B/V + C/V² + …
• B, C = virial coefficients

Compressibility Factor

• Z = PV/nRT
• For ideal gas: Z = 1

Fluid Mechanics

Fluid Statics

Pressure Variation with Height

• ΔP = ρgΔh
• ρ = fluid density
• g = gravitational acceleration
• Δh = height difference

Hydrostatic Force on a Submerged Surface

• F = ρgh_c A
• h_c = depth to centroid
• A = surface area

Fluid Dynamics

Bernoulli’s Equation

• P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
• P = pressure
• v = velocity
• h = height

Continuity Equation

• ṁ = ρ₁A₁v₁ = ρ₂A₂v₂
• ṁ = mass flow rate
• A = cross-sectional area

Reynolds Number

• Re = ρvD/μ = vD/ν
• D = characteristic length
• μ = dynamic viscosity
• ν = kinematic viscosity

Flow Regimes:

• Re < 2300: Laminar flow
• 2300 < Re < 4000: Transitional
• Re > 4000: Turbulent flow

Pumps and Pipelines

Energy Balance in Pipe Systems

• (P₁/ρg + v₁²/2g + z₁) + hₚ = (P₂/ρg + v₂²/2g + z₂) + hᴌ
• hₚ = pump head
• hᴌ = head loss

Friction Factor and Head Loss

• For laminar flow: f = 64/Re
• For turbulent flow: 1/√f = -2log(ε/3.7D + 2.51/Re·√f) (Colebrook equation)
• Head loss: hᴌ = f(L/D)(v²/2g)
• ε = pipe roughness
• L = pipe length

Pump Power

• P = ρgQH/η
• Q = volumetric flow rate
• H = pump head
• η = pump efficiency

Heat Transfer

Modes of Heat Transfer

Conduction

• q = -kA(dT/dx)
• q = heat transfer rate (W)
• k = thermal conductivity (W/m·K)
• A = cross-sectional area (m²)
• dT/dx = temperature gradient (K/m)

Convection

• q = hA(Ts – T∞)
• h = convective heat transfer coefficient (W/m²·K)
• Ts = surface temperature
• T∞ = fluid temperature

Radiation

• q = εσA(Ts⁴ – Tsurr⁴)
• ε = emissivity
• σ = Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²·K⁴)
• Tsurr = surrounding temperature

Heat Exchangers

Logarithmic Mean Temperature Difference (LMTD)

• LMTD = (ΔT₁ – ΔT₂)/ln(ΔT₁/ΔT₂)
• For counter-flow: ΔT₁ = Th,in – Tc,out, ΔT₂ = Th,out – Tc,in
• For parallel flow: ΔT₁ = Th,in – Tc,in, ΔT₂ = Th,out – Tc,out

Heat Transfer Rate

• Q = UA·LMTD
• U = overall heat transfer coefficient
• A = heat transfer area

Effectiveness-NTU Method

• ε = actual heat transfer / maximum possible heat transfer
• NTU = UA/Cmin
• Cmin = (ṁcp)min

Mass Transfer

Fick’s Laws of Diffusion

First Law (Steady State)

• J = -D(dC/dx)
• J = diffusion flux (mol/m²·s)
• D = diffusion coefficient (m²/s)
• dC/dx = concentration gradient (mol/m⁴)

Second Law (Unsteady State)

• dC/dt = D(d²C/dx²)

Mass Transfer Coefficients

• NA = kc(CA,s – CA,∞)
• NA = mass transfer rate of A
• kc = mass transfer coefficient
• CA,s = concentration at surface
• CA,∞ = concentration in bulk fluid

Dimensionless Numbers

• Schmidt Number: Sc = μ/ρD
• Sherwood Number: Sh = kcL/D
• Peclet Number: Pe = vL/D

Reaction Engineering

Reaction Rate

• rA = -dCA/dt = k·f(CA, CB, …)
• k = rate constant
• f() = function of concentrations

Arrhenius Equation

• k = A·e^(-Ea/RT)
• A = pre-exponential factor
• Ea = activation energy
• R = gas constant
• T = absolute temperature

Reactor Design Equations

Batch Reactor

• dCA/dt = rA
• t = ∫(dCA/rA) from CA0 to CA

Continuous Stirred Tank Reactor (CSTR)

• V = FA0(XA)/(-rA)
• V = reactor volume
• FA0 = molar flow rate of A
• XA = conversion of A

Plug Flow Reactor (PFR)

• V = FA0∫(dXA/(-rA)) from 0 to XA
• dV/dXA = FA0/(-rA)

Catalysis

• Rate = k·[catalyst]·f(reactants)
• Catalyst lowers activation energy without being consumed

Separation Processes

Distillation

Relative Volatility

• α = (yA/xA)/(yB/xB)
• yA, yB = vapor phase compositions
• xA, xB = liquid phase compositions

McCabe-Thiele Method

• Operating lines: y = (L/V)x + (F/V)
• L = liquid flow rate
• V = vapor flow rate
• F = feed flow rate

Minimum Reflux Ratio

• (L/D)min = xD(1-xF)/(xF(1-xD))
• xD = distillate composition
• xF = feed composition

Extraction

Distribution Coefficient

• KD = concentration in extract / concentration in raffinate

Number of Stages

• For countercurrent extraction with constant KD:
• N = ln[(Rout – mSin)/(Rin – mSin)]/ln[(L + mV)/L]
• R = raffinate concentration
• S = solvent concentration
• m = distribution coefficient
• L, V = flow rates

Absorption/Stripping

Height of a Transfer Unit (HTU)

• HTU = L/KLa or V/KGa
• KLa, KGa = volumetric mass transfer coefficients

Number of Transfer Units (NTU)

• NTU = ∫(dx/(y* – y)) from bottom to top
• y* = equilibrium vapor composition

Process Control

Transfer Functions

First-order System

• G(s) = K/(τs + 1)
• K = gain
• τ = time constant

Second-order System

• G(s) = K/(τ²s² + 2ζτs + 1)
• ζ = damping coefficient

PID Controllers

Controller Equation

• u(t) = Kp·e(t) + Ki∫e(t)dt + Kd·de(t)/dt
• u(t) = controller output
• e(t) = error = setpoint – measured value
• Kp = proportional gain
• Ki = integral gain
• Kd = derivative gain

Tuning Methods

Ziegler-Nichols Method:

• Ku = ultimate gain
• Pu = ultimate period

Process Design & Economics

Capital Cost Estimation

Six-Tenths Rule

• Cost₂ = Cost₁(Size₂/Size₁)^0.6

Lang Factor

• Fixed capital investment = Σ(equipment costs) × Lang factor
• For solid processing plants: Lang factor ≈ 3.1
• For fluid processing plants: Lang factor ≈ 4.7
• For mixed processing plants: Lang factor ≈ 3.6

Operating Cost Estimation

Manufacturing Costs

• Direct production costs
• Fixed charges
• Plant overhead costs
• General expenses

Profitability Analysis

• Payback period = Total capital investment / Annual cash flow
• Return on investment (ROI) = (Annual profit / Total capital investment) × 100%
• Net present value (NPV) = Σ[CFt/(1+r)^t] – Initial investment
• Internal rate of return (IRR): r when NPV = 0

Safety & Environmental

Hazard Analysis

HAZOP (Hazard and Operability Study)

• Systematic examination of process deviations
• Guide words: No, More, Less, As Well As, Part Of, Reverse, Other Than

Risk Assessment Matrix

• Likelihood × Consequence = Risk level

Emission Control

Air Pollution Control Efficiency

• Efficiency = (inlet concentration – outlet concentration) / inlet concentration × 100%

Wastewater Treatment Parameters

• BOD (Biochemical Oxygen Demand)
• COD (Chemical Oxygen Demand)
• TOC (Total Organic Carbon)
• TSS (Total Suspended Solids)

Common Chemical Processes

Petrochemicals

• Crude oil distillation
• Catalytic cracking
• Reforming
• Alkylation

Polymers

• Addition polymerization
• Condensation polymerization
• Injection molding
• Extrusion

Biochemical

• Fermentation
• Enzymatic reactions
• Bioreactors
• Downstream processing (filtration, chromatography)

Resources for Further Learning

Professional Organizations

• American Institute of Chemical Engineers (AIChE)
• Institution of Chemical Engineers (IChemE)
• Society of Chemical Industry (SCI)

Key Reference Books

• Perry’s Chemical Engineers’ Handbook
• Coulson and Richardson’s Chemical Engineering
• Unit Operations of Chemical Engineering (McCabe)
• Chemical Process Safety (Crowl and Louvar)

Online Resources

• National Institute of Standards and Technology (NIST)
• Chemical Engineering World
• MIT OpenCourseWare – Chemical Engineering
• Process Engineering Associates Technical Resources

This cheatsheet provides a comprehensive reference for chemical engineering fundamentals. Always verify calculations and consult detailed references for specific applications.