PEC EPE Chemical cheat sheet

Overall mass balance: accumulation = sum of inlet mass flows - sum of outlet mass flows + generation - consumption; accumulation is zero at steady state.

Component balance for a well-mixed control volume: d(V C_i)/dt = sum(F_in C_i,in) - sum(F_out C_i,out) + r_i V; at steady state the derivative term is zero.

Open-system steady energy balance: Q - W_s = sum_out m(h + v^2/2 + gz) - sum_in m(h + v^2/2 + gz); kinetic and potential terms are often negligible.

Closed-system first law: Delta U = Q - W; enthalpy is H = U + PV, and for an ideal gas Cp - Cv = R.

Ideal-gas equation of state: PV = nRT; for an ideal gas Delta H = integral Cp dT and Delta U = integral Cv dT.

Second law: Delta S_universe >= 0; for a reversible process Delta S = Q_rev/T, and entropy generation is positive for real processes.

Gibbs free energy: Delta G = Delta H - T Delta S; at constant T and P a negative Delta G indicates spontaneity, and equilibrium gives Delta G = 0.

Equilibrium constant: K = exp(-Delta G_standard/RT); gas-phase K is expressed with fugacities or partial pressures, and liquid-phase K with activities.

Standard heat of reaction: Delta H_rxn_standard = sum(nu_i Delta H_f,i_standard); formation enthalpies of elements in their standard states are zero.

Reynolds number for a circular pipe: Re = rho v D / mu = 4 m_dot / (pi D mu); Re < 2100 is laminar and Re > 4000 is turbulent.

Darcy-Weisbach pressure drop: Delta P = f (L/D)(rho v^2/2); laminar friction factor f = 64/Re, while turbulent f depends on Re and relative roughness.

Bernoulli equation with pump work and head loss: p1/(rho g) + v1^2/(2g) + z1 + h_pump = p2/(rho g) + v2^2/(2g) + z2 + h_loss.

Pump NPSH available: NPSHA = (p_atm - p_vap)/(rho g) + z_s - h_f,suction, where z_s is liquid level above pump centerline; NPSHA must exceed NPSHR.

Fourier conduction: q = -k A dT/dx; plane-wall resistance R = L/(kA), cylindrical-wall resistance R = ln(r2/r1)/(2 pi k L).

Convection and overall heat transfer: q = h A (T_s - T_inf); 1/(U A) includes convective, fouling, and wall resistances; q = U A F Delta T_lm.

Effectiveness-NTU: epsilon = q/q_max and NTU = U A/C_min; counterflow has higher effectiveness than parallel flow for the same NTU and C_r.

Pump affinity laws at constant impeller diameter: Q proportional to N, H proportional to N^2, and power proportional to N^3.

Natural convection: Gr = g beta Delta T L^3/nu^2, Ra = Gr Pr, and Nu = C Ra^n; forced convection correlations use Nu = C Re^m Pr^n.

Fick's first law: J_A = -D_AB dC_A/dx; the negative sign indicates diffusion from higher to lower concentration.

Film mass transfer: N_A = k_c (C_Ai - C_A); Sherwood number Sh = k_c L/D, and correlations take Sh as a function of Re and Sc.

Vapor-liquid equilibrium: Raoult's law p_i = x_i p_i^sat, Dalton's law y_i = p_i/P, and relative volatility alpha_ij = (y_i/x_i)/(y_j/x_j).

Flash calculation: Rachford-Rice equation sum z_i (1 - K_i)/(1 + beta (K_i - 1)) = 0, where beta is vapor fraction and K_i = y_i/x_i.

McCabe-Thiele rectifying line: y = (R/(R+1)) x + x_D/(R+1); the q-line locates the feed condition, and minimum reflux corresponds to a pinch on the equilibrium curve.

Kremser absorption: stage count depends on absorption factor A = L/(mG); higher A and more stages reduce solute in the exiting gas for a fixed lean-oil rate.

Rate-based separation: NTU = integral dY/(Y - Y*) and HTU = G/K_y a; packed height Z = NTU times HTU.

Langmuir isotherm: q = q_max K p/(1 + K p); at low p loading is linear, and at high p it approaches monolayer saturation.

Membrane flux J = P Delta p/delta; ideal selectivity alpha_ij = (y_i/y_j)/(x_i/x_j), and actual selectivity is reduced by back diffusion and pressure losses.

Power-law rate: -r_A = k C_A^n; reaction order n is experimental, not necessarily the stoichiometric coefficient.

Arrhenius temperature dependence: k = A exp(-Ea/RT); a plot of ln k versus 1/T has slope -Ea/R.

Batch reactor time: t = N_A0 integral_0^X dX/(-r_A V); for constant volume and density, t = C_A0 integral dX/(-r_A).

CSTR design equation at steady state: V = F_A0 X/(-r_A), with -r_A evaluated at the outlet concentration and temperature.

PFR design equation: V = F_A0 integral_0^X dX/(-r_A); for a packed bed, catalyst weight W = F_A0 integral dX/(-r_A').

Space time tau = V/v0 and space velocity SV = 1/tau; space time is not the same as actual mean residence time when density changes.

Adiabatic reactor temperature rise: T = T0 + (-Delta H_rxn) X / sum(F_i Cp_i); exothermic reactions raise temperature and can reduce equilibrium conversion.

Selectivity and yield: selectivity = desired product formed / undesired product formed; yield = desired product formed / reactant fed; both depend on conversion and kinetics.

Thiele modulus phi = L sqrt(k/D_e); effectiveness factor eta = actual rate/rate without pore diffusion, and eta approaches 1 when phi is small.

NPV = sum CF_t/(1+i)^t - initial investment; a positive NPV means the project return exceeds the discount rate, and IRR is the i that makes NPV zero.

Payback period = initial investment/annual net cash flow; discounted payback replaces raw cash flows with discounted cash flows.

Six-tenths rule: C2 = C1 (S2/S1)^0.6; the exponent typically ranges from 0.5 to 0.8 for similar equipment and modest capacity changes.

Break-even quantity = fixed costs/(unit price - unit variable cost); contribution margin per unit is price minus variable cost.

PFD shows major equipment, streams, and mass/energy balance data; a P&ID adds instruments, control loops, interlocks, and piping details.

Degrees of freedom = number of independent variables - number of independent equations; a flowsheet is exactly specified when this count is zero.

Sequential modular simulation solves units in flow order with recycle convergence loops; equation-oriented simulation solves all model equations simultaneously and handles recycles and optimization well.

Pinch analysis identifies the minimum utility target from composite curves; heat transfer across the pinch increases utility demand, and Delta T_min trades capital against energy cost.

Capital cost estimate accuracy improves from order-of-magnitude to definitive as design detail increases; contingency covers remaining uncertainty.

Flammability limits are fuel concentrations in air between LEL and UEL; below LEL the mixture is too lean, and above UEL it is too rich to ignite.

Flash point is the lowest temperature at which a liquid gives a flammable vapor near its surface; autoignition temperature is the temperature of spontaneous ignition without an ignition source.

HAZOP examines nodes with guidewords such as no, more, less, reverse, and as well as; each deviation is evaluated for causes, consequences, and safeguards.

LOPA: mitigated event frequency = initiating event frequency times the product of independent protection-layer PFDs; compare the result with the tolerable risk target.

Low-demand SIL PFD average ranges: SIL 1 = 1e-2 to 1e-1, SIL 2 = 1e-3 to 1e-2, SIL 3 = 1e-4 to 1e-3, and SIL 4 = 1e-5 to 1e-4.

Relief valve set pressure is at or below MAWP; API 520 sizing uses required relieving capacity, allowable overpressure, and fluid properties to select orifice area.

Inherent safety order: minimize, substitute, moderate, and simplify; engineered safeguards, procedures, and PPE are added after inherent options are exhausted.

Exposure limits: TLV-TWA is an 8-hour time-weighted average, STEL is a 15-minute short-term limit, and IDLH is immediately dangerous to life or health.

Risk is commonly frequency times consequence; ALARP means risk is reduced as low as reasonably practicable, with residual risk documented and monitored.

Ideal PID: u = Kc [e + (1/tau_I) integral e dt + tau_D de/dt]; integral action removes steady-state offset and derivative action adds anticipation.

Proportional band PB = 100/Kc percent; a smaller PB means higher controller gain and a more aggressive response.

First-order plus dead time model: tau_p dy/dt + y = Kp u(t - theta); dead time theta limits achievable gain and causes phase lag.

Ziegler-Nichols ultimate-cycle PID settings: Kc = 0.6 Ku, tau_I = Pu/2, tau_D = Pu/8, where Ku is ultimate gain and Pu is ultimate period.

Cascade control uses a primary controller output as the setpoint of a faster secondary controller; the inner loop rejects disturbances before they reach the primary variable.

Feedforward control measures a disturbance and applies a model-based correction; it is combined with feedback to handle model error and unmeasured disturbances.

A 4-20 mA transmitter uses 4 mA as live zero and 20 mA as span; a current below about 3.6 mA usually indicates an open circuit or fault.

Control valve fail-safe action is fail-closed, fail-open, or fail-last; the choice follows the safe process state on loss of air or signal.

Equal-percentage valve trim changes flow more sharply at high lift than linear trim; cavitation and flashing are avoided by checking vena contracta pressure against vapor pressure.

Carbon steel relies on a protective oxide scale; austenitic stainless steels rely on a chromium-rich passive film and are susceptible to chloride stress corrosion cracking above roughly 60 C.

Galvanic corrosion occurs when dissimilar metals contact an electrolyte; the more active metal is anodic, and a small anode with a large cathode produces rapid localized attack.

Nernst equation: E = E_standard - (RT/nF) ln Q; Pourbaix diagrams map stable phases as functions of potential and pH.

ASME Section VIII governs pressure-vessel design; ASME B31.3 governs process piping; both require design pressure, design temperature, and allowable stress limits.

Minimum design metal temperature is the lowest temperature allowed without brittle-fracture controls; impact testing or a tougher material is required below it.

Stress is force divided by area and strain is deformation divided by original length; yield strength marks the onset of permanent deformation, and creep occurs at elevated temperature under sustained load.

Corrosion allowance adds thickness to compensate for expected metal loss; erosion-corrosion risk rises with velocity, entrained solids, and turbulent fittings.

Cathodic protection supplies electrons from sacrificial anodes or an impressed-current system; it is often combined with coating to reduce the required current.

Material selection: carbon steel suits many dry hydrocarbon and neutral aqueous services; duplex stainless steels resist chloride SCC better than 304/316, while nickel alloys are used for severe acids.