Registered Chemical Engineer cheat sheet

Material balance on a steady-state unit: accumulation = 0, so Σ(in) = Σ(out) + consumption − generation; for a nonreacting splitter, component balances close independently of total mass.

Recycle with purge: overall conversion fixes fresh feed; single-pass conversion fixes recycle ratio R = (overall − single-pass)/(single-pass × (1 − overall)); purge prevents inert buildup at steady state when inert in feed > 0.

Energy balance for steady flow: Q − W_s = Σ out n_i h_i − Σ in n_i h_i; use reference-state enthalpies consistently and include heat of reaction once via ΔH_rxn at the reference temperature.

Laminar flow in a circular pipe: f = 64/Re, ΔP = 128μLQ/(πD⁴) (Hagen–Poiseuille); turbulent friction factor from Colebrook or Blasius f = 0.316Re^(−0.25) for smooth pipes, Re < 10⁵.

Pump power: W_pump = Q·ΔP/η; system head includes static lift, friction (Darcy–Weisbach h_f = f(L/D)(v²/2g)), and minor losses ΣK(v²/2g). NPSH_a must exceed NPSH_r to avoid cavitation.

Heat transfer: Q = UAΔT_lm with F correction for multipass; ΔT_lm = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂); overall U from 1/UA = 1/(h_iA_i) + R_f + wall resistance + 1/(h_oA_o).

Conduction: steady 1-D slab Q = kAΔT/L; cylinder Q = 2πkLΔT/ln(r₂/r₁); sphere Q = 4πkΔT/(1/r₁ − 1/r₂). Lumped capacitance valid when Bi = hL/k < 0.1.

Mass transfer and drying/absorption: Fick's law J = −D dC/dx; film theory k_c = D/δ; for dilute absorption, mole fraction change follows log-mean driving force; NTU = (y_in − y_out)/Δy_lm.

Reaction kinetics: Arrhenius k = A exp(−E/RT); first-order conversion X = 1 − exp(−kt) in batch; CSTR volume V = F_A0 X/(−r_A); PFR volume V = F_A0 ∫dX/(−r_A); selectivity favors CSTR for series reactions, PFR for parallel reactions with higher-order desired path.

Distillation: McCabe–Thiele operating lines y = (R/(R+1))x + x_D/(R+1) for rectifying; q-line slope q/(q−1); minimum reflux from pinch at q-line/equilibrium intersection; Fenske gives N_min at total reflux.

Minimum fluidization: at u_mf, ΔP = (1 − ε_mf)(ρ_s − ρ_g)gL; Ergun equation relates u_mf to particle diameter and sphericity. Terminal velocity from drag balance; elutriation when u > u_t.

Dimensional analysis: Buckingham Pi gives number of groups = variables − fundamental dimensions; common groups include Re = ρvD/μ, Nu = hD/k, Pr = C_pμ/k, Sc = μ/(ρD_AB), Sh = k_cD/D_AB, Bi = hL/k.

Control: first-order plus dead time process G = K_p e^(−θs)/(τs + 1); ultimate gain and period from Ziegler–Nichols closed-loop tuning; PID integral action eliminates offset, derivative action adds lead for stability.

Thermodynamics: fugacity coefficient from departure functions; Raoult's law for ideal VLE y_iP = x_iP_i^sat; relative volatility α = K_i/K_j; azeotrope where α = 1 and x = y.

Economics and sizing: six-tenths rule C₂ = C₁(S₂/S₁)^0.6; payback = fixed capital/annual cash flow; NPV = Σ CF_t/(1+r)^t − capital; choose the alternative with positive NPV and highest NPV at the given hurdle rate.

Safety and relief: relief valve sized from API 520 orifice equations using required relieving rate; two-phase flow may require DIERS methods. LEL/UEL bound flammable operation; inerting keeps O₂ below limiting oxygen concentration.