Registered Chemical Engineer flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Recycle ratio formula

R = (X_overall − X_single)/(X_single(1 − X_overall)). Overall conversion determines fresh feed and product; single-pass conversion determines recycle flow around the reactor.

Hagen–Poiseuille equation

For laminar flow in a circular pipe, ΔP = 128μLQ/(πD⁴) and friction factor f = 64/Re. Pressure drop scales with the fourth power of diameter.

Darcy–Weisbach friction loss

Head loss h_f = f(L/D)(v²/2g). Minor losses add ΣK(v²/2g). Friction factor from Colebrook, or Blasius f = 0.316Re^(−0.25) for smooth pipes.

NPSH and cavitation

Net positive suction head available must exceed that required by the pump. NPSH_a = (P_suction − P_vapor)/(ρg) plus velocity head; falling short causes cavitation and impeller damage.

Log mean temperature difference

ΔT_lm = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂) for countercurrent or single-pass exchangers. For multipass shells multiply by correction factor F from charts.

Overall heat transfer coefficient

1/UA = 1/(h_iA_i) + R_f,i/A_i + wall resistance + R_f,o/A_o + 1/(h_oA_o). The largest resistance controls the design; fouling often dominates.

Biot number criterion

Bi = hL/k compares internal conduction resistance to external convection. When Bi < 0.1, temperature is nearly uniform and lumped capacitance analysis applies.

Arrhenius rate constant

k = A exp(−E/RT). Plotting ln k versus 1/T gives slope −E/R. Activation energy controls sensitivity of rate to temperature.

CSTR design equation

V = F_A0 X/(−r_A) evaluated at exit conditions. CSTR operates at the lowest rate in the reactor, so it requires more volume than a PFR for positive-order kinetics.

PFR design equation

V = F_A0 ∫₀^X dX/(−r_A). For first-order isothermal reaction, X = 1 − exp(−kτ). PFR achieves higher conversion than CSTR for the same volume.

Selectivity in series reactions

For A→B→C, a CSTR keeps B concentration low, favoring B yield; a PFR builds B along the length, increasing overreaction. Choose reactor accordingly.

McCabe–Thiele operating line

Rectifying line: y = (R/(R+1))x + x_D/(R+1). Stripping line passes through (x_B, x_B). q-line slope q/(q−1) represents feed thermal condition.

Fenske minimum stages

N_min = ln[(x_D/(1−x_D))·((1−x_B)/x_B)]/ln α_avg at total reflux. Gives minimum theoretical stages independent of reflux ratio.

Relative volatility

α_ij = K_i/K_j = (y_i/x_i)/(y_j/x_j). Larger α means easier separation. An azeotrope occurs where α = 1 and vapor composition equals liquid composition.

Raoult's law VLE

y_iP = x_iP_i^sat for ideal mixtures. Valid at low pressure when components are chemically similar. Deviations require activity coefficients from models like NRTL.

Minimum fluidization velocity

At u_mf, bed pressure drop equals weight per area: ΔP = (1−ε_mf)(ρ_s−ρ_g)gL. Ergun equation links u_mf to particle size, sphericity, and voidage.

Buckingham Pi theorem

Number of dimensionless groups equals variables minus independent dimensions. Used to derive Re, Nu, Pr, Sc, Sh, and Bi from governing variables.

Reynolds number definition

Re = ρvD/μ for pipe flow. Re < 2100 laminar, 2100–4000 transitional, above 4000 turbulent. Determines friction factor and heat transfer correlations.

Prandtl and Schmidt numbers

Pr = C_pμ/k compares momentum to thermal diffusivity. Sc = μ/(ρD_AB) compares momentum to mass diffusivity. Both appear in convection correlations.

Lumped capacitance cooling

For Bi < 0.1, (T − T_∞)/(T₀ − T_∞) = exp(−hAt/(ρVC_p)). Time constant τ = ρVC_p/(hA) sets the response speed.

Ziegler–Nichols tuning

From ultimate gain K_u and period P_u, PID settings are K_c = 0.6K_u, τ_I = P_u/2, τ_D = P_u/8. Gives quarter-amplitude decay, often aggressive.

First-order plus dead time

Model G = K_p exp(−θs)/(τs+1). Dead time θ limits achievable controller gain; ratio θ/τ indicates controllability. Larger ratio means harder control.

Six-tenths rule

Capital cost scales as C₂ = C₁(S₂/S₁)^0.6. Exponent near 0.6 reflects economy of scale; adjust for location, time, and material factors.

Net present value

NPV = Σ CF_t/(1+r)^t − capital. Accept projects with NPV > 0 at the hurdle rate r. Higher NPV indicates greater value creation.

Payback period

Payback = fixed capital investment / annual net cash flow. Simple measure ignoring time value of money; useful as a quick risk screen.

Relief valve sizing

Required relieving area from API 520 orifice equations using mass flux and set pressure. Two-phase relief may need DIERS methodology when vapor and liquid coexist.

Flammability limits

LEL and UEL bound the flammable concentration range in air. Inerting keeps oxygen below the limiting oxygen concentration to prevent ignition.

Fugacity coefficient

φ_i = f_i/(y_iP), from departure functions or an equation of state. For ideal gas φ = 1. Used in VLE when nonideal gas behavior matters.

Heat of reaction via Hess

ΔH_rxn at temperature T = Σν_i h_i(T). Use standard heats of formation at reference temperature plus sensible heat corrections for products and reactants.

Fick's first law

J_A = −D_AB dC_A/dx. Molar flux is proportional to concentration gradient. Film theory gives k_c = D/δ for the mass transfer coefficient.

Number of transfer units

NTU = (y_in − y_out)/Δy_lm for dilute absorption. Higher NTU means more mass transfer duty. Related to column height by H = HTU·NTU.

Pump hydraulic power

W_pump = Q·ΔP/η, where Q is volumetric flow and η is efficiency. Brake power divides by motor efficiency. System head includes lift and friction.