UPDA Chemical cheat sheet

Reynolds number Re = ρvD/μ = vD/ν; laminar pipe flow Re < 2100, turbulent Re > 4000.

Bernoulli (frictionless, steady, incompressible): P1/ρ + v1²/2 + gz1 = P2/ρ + v2²/2 + gz2.

Darcy–Weisbach friction loss: hf = f (L/D)(v²/2g); for laminar flow f = 64/Re.

Newton's method: x_{n+1} = x_n − f(x_n)/f'(x_n); quadratic convergence near a simple root.

Trapezoid rule error is O(h²); Simpson's 1/3 rule error is O(h⁴) and needs an even number of intervals.

Dimensional analysis: number of independent dimensionless groups = n variables − m fundamental dimensions (Buckingham Pi).

Linear least squares slope/intercept from Σx, Σy, Σxy, Σx²: b = (nΣxy − ΣxΣy)/(nΣx² − (Σx)²).

Common dimensionless groups: Re, Pr = cpμ/k, Nu = hD/k, Sc = μ/(ρD_AB), Sh = k_c D/D_AB, Bi = hL/k_s.

General balance: Accumulation = In − Out + Generation − Consumption; at steady state accumulation = 0.

Degrees of freedom = number of unknowns − number of independent equations; a well-posed steady-state problem has 0.

Basis selection: choose 100 mol or 100 kg of a feed stream to simplify fractional compositions.

Overall and component balances are independent only up to the number of components; use atomic balances for reacting systems.

Extent of reaction ξ: n_i = n_i0 + ν_i ξ; independent reactions found from rank of the atom matrix.

Energy balance for steady open system: Q − W = Σ n_out h_out − Σ n_in h_in (neglect KE/PE).

Heat of reaction at T from ΔH_r(T) = ΔH_r(T_ref) + ∫Σν_i cp_i dT (Kirchhoff).

Combustion: theoretical O2 from stoichiometry; excess air % = (O2 supplied − O2 theoretical)/O2 theoretical × 100.

Recycle and purge: purge prevents accumulation of inert or trace components; recycle raises overall conversion.

First law closed system: ΔU = Q − W; for reversible path W = ∫P dV.

Entropy change: ΔS = ∫dQ_rev/T; ΔS_universe ≥ 0 (second law).

Carnot efficiency η = 1 − T_C/T_H (absolute temperatures).

Raoult's law: y_i P = x_i P_i^sat; modified Raoult: y_i P = x_i γ_i P_i^sat.

Antoine equation: ln P^sat = A − B/(T + C) with T in the correlation's stated units.

Fugacity coefficient φ_i = f_i/(y_i P); ideal gas φ_i = 1; equilibrium K_i = y_i/x_i = γ_i P_i^sat/(φ_i P).

Gibbs phase rule: F = C − P + 2 (degrees of freedom, components, phases).

Activity coefficient models: Margules/van Laar for binary; Wilson, NRTL, UNIQUAC for partially miscible systems.

Clausius–Clapeyron: ln(P2/P1) = −(ΔH_vap/R)(1/T2 − 1/T1).

Newtonian shear stress τ = μ (du/dy); viscosity units 1 Pa·s = 1000 cP.

Continuity for incompressible flow in a pipe: Q = A1v1 = A2v2.

Pump power: P = ρ g Q H / η; head H in metres of flowing fluid.

NPSH available = (P_atm − P_vap)/(ρg) + z − h_f,suction; must exceed NPSH required.

Ergun equation for packed beds combines viscous (150) and inertial (1.75) terms with void fraction ε.

Fanning friction factor f_F = 0.25 of Darcy f; f_F = 16/Re in laminar pipe flow.

Equivalent length method converts fittings to L_eq/D values added to pipe length for pressure drop.

Centrifugal pump curves: operating point is intersection of pump curve and system curve; affinity laws Q∝N, H∝N², P∝N³.

Fourier's law: q = −k A dT/dx; plane wall R = L/(kA).

Convection: q = h A ΔT; Nu correlations: Dittus–Boelter Nu = 0.023 Re^0.8 Pr^n (n = 0.4 heating, 0.3 cooling).

Overall coefficient: 1/U = 1/h_i + R_fi + (t/k) + R_fo + 1/h_o (area basis must be consistent).

LMTD = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2); q = U A F ΔT_lm.

Effectiveness–NTU: ε = q/q_max; NTU = UA/C_min; C_r = C_min/C_max.

Radiation: q = ε σ A (T_s⁴ − T_surr⁴), σ = 5.67×10⁻⁸ W/(m²·K⁴).

Boiling/dropwise condensation coefficients are much larger than film condensation; fouling reduces U over time.

Biot number Bi = hL/k_s controls internal vs external resistance; Bi < 0.1 lumped capacitance valid.

Fick's law: J_A = −D_AB dc_A/dx; steady film flux N_A = k_c (c_A1 − c_A2).

Sherwood correlations: Sh = 0.023 Re^0.83 Sc^0.33 for turbulent pipe flow.

Distillation: relative volatility α = K_light/K_heavy; Fenske N_min = log[(xD/(1−xD))((1−xB)/xB)]/log α.

Minimum reflux via pinch point; operating lines from material balances on rectifying and stripping sections.

Absorption/stripping: Kremser equations relate stages, absorption factor A = L/(mV).

Extraction: distribution coefficient K = y/x; selectivity is ratio of distribution coefficients.

Drying: constant-rate period flux controlled by external conditions; falling-rate by internal diffusion.

Membrane/ultrafiltration: flux J = ΔP/(μ R_m); rejection = 1 − c_permeate/c_feed.

Batch: −dC_A/dt = k C_A^n; first order gives ln(C_A0/C_A) = kt.

CSTR design: V = F_A0 X / (−r_A); performance equation uses exit conditions.

PFR design: V = F_A0 ∫ dX/(−r_A) from 0 to X.

Arrhenius: k = A exp(−E_a/RT); doubling rule ~10 °C gives roughly 2–3× rate near ambient.

Space time τ = V/v0; space velocity SV = 1/τ.

Selectivity and yield: S = moles desired/(moles undesired); Y = moles desired/(moles reactant fed).

Multiple reactions: maximize selectivity by adjusting concentration ratios, temperature, and reactor type (CSTR vs PFR).

Catalysis: turnover frequency = molecules converted per active site per time; Thiele modulus and effectiveness factor η.

Non-ideal flow: residence time distribution E(t); mean residence time t̄ = V/Q.

First-order transfer function G(s) = K/(τs + 1); step response reaches 63.2% at t = τ.

Second-order: G(s) = K ω_n²/(s² + 2ζω_n s + ω_n²); underdamped if 0 < ζ < 1.

PID: u(t) = K_p e + K_i ∫e dt + K_d de/dt; standard form uses integral time τ_I and derivative time τ_D.

Closed-loop characteristic equation 1 + G_c G_p = 0 determines stability; Routh–Hurwitz test for roots.

Ultimate gain and period (Ziegler–Nichols) give tuning: K_p = 0.6 K_u, τ_I = P_u/2, τ_D = P_u/8 for PID.

Dead time (transport lag) e^{−θs} degrades stability; Smith predictor compensates.

Control valve: fail-safe action, equal-percentage vs linear trim; valve sizing uses C_v.

Measurement: thermocouple Seebeck effect; orifice plate flow ∝ √ΔP; level by differential pressure.

Capital cost scaling: C2 = C1 (Q2/Q1)^n; n ≈ 0.6 (six-tenths rule).

Chemical Engineering Plant Cost Index adjusts costs: C2 = C1 (I2/I1).

Payback period = fixed capital / annual cash flow; simple and ignores time value.

NPV = Σ CF_t/(1 + r)^t − initial investment; accept if NPV > 0.

IRR is the discount rate where NPV = 0; compare to hurdle rate.

Depreciation: straight-line (P − S)/n; MACRS uses accelerated recovery periods.

Profitability: ROI, discounted cash flow rate of return, and break-even analysis (fixed vs variable costs).

Project management: critical path method (CPM) determines longest path through network; float = LS − ES.

Flash point, fire point, autoignition temperature define flammability hazards; LFL/UFL bound explosive range.

Dust and vapor explosions require fuel, oxygen, ignition, dispersion, and confinement.

HAZOP uses guide words (no, more, less, reverse, as well as, part of, other than) on nodes and parameters.

LOPA and safety integrity level (SIL) quantify risk reduction from independent protection layers.

Toxic exposure: TLV-TWA, STEL, and IDLH values; use PEL for regulatory limits.

Ethics: hold paramount public safety, health, and welfare; disclose conflicts; report known violations to appropriate authority.

Environmental: BOD/COD measure organic load; permits and emission limits govern discharge; waste hierarchy reduce > reuse > recycle > recover > dispose.

Pressure relief: relief valve for thermal expansion, rupture disc for fast pressure rise; relief sizing per API 520/521.

Linear system Ax = b solvable if det(A) ≠ 0; condition number κ(A) = ||A|| ||A⁻¹|| measures sensitivity.

Newton–Raphson converges quadratically for simple roots; secant method superlinear without derivative.

Bisection guarantees convergence but is slow (linear); error halves each iteration.

Euler method first-order ODE: y_{n+1} = y_n + h f(t_n, y_n); error O(h).

Runge–Kutta 4th order local error O(h⁵), global O(h⁴).

Partial differential equations: explicit finite difference stability requires CFL condition (e.g., αΔt/Δx² ≤ 0.5 for 1-D heat).

Roots of polynomials: Descartes' rule of signs and synthetic division; real roots for physical solutions.

Statistical process control: control charts use ±3σ limits; Cpk = min(USL−μ, μ−LSL)/(3σ).

Risk = probability × consequence; risk matrix ranks hazards as low/medium/high.

Fault tree analysis: top event probability via AND (product) and OR (sum) gates.

Event tree analysis branches from initiating event to outcomes; combines with fault trees for QRA.

Bow-tie diagram links threats through preventive barriers to top event and recovery barriers to consequences.

Consequence modeling: Gaussian plume dispersion, BLEVE, pool fire, and vapor cloud explosion.

Inherent safety hierarchy: minimize, substitute, moderate, simplify.

Layer of protection analysis: independent protection layers reduce frequency; each layer must be independent and auditable.

Safety instrumented system: SIL 1–4 based on PFD ranges; SIL 4 most stringent.

Total capital investment = fixed capital + working capital; working capital typically 10–20% of fixed.

Total product cost = manufacturing cost + general expenses; manufacturing includes raw materials, utilities, labor, depreciation.

Utilities: steam, cooling water, electricity, refrigeration; cost varies with temperature/pressure level.

Cost of manufacturing (COM) = 0.28 FCI + 2.73 C_OL + 1.23 (C_UT + C_WT + C_RM).

Break-even point: Q* = F/(P − V); contribution margin = P − V per unit.

Sensitivity analysis tests NPV against changes in price, raw material, capacity, and discount rate.

Time value of money: F = P(1 + i)^n; annuity factor = [(1 + i)^n − 1]/[i(1 + i)^n].

Cost of capital: weighted average of debt and equity; used as discount rate for NPV.

Corrosion types: uniform, galvanic, crevice, pitting, stress corrosion cracking, erosion-corrosion.

Galvanic series ranks metals; dissimilar metals in electrolyte cause accelerated attack of the more active metal.

Cathodic protection: sacrificial anode or impressed current; protects by making structure cathodic.

Coatings and inhibitors: barrier protection; passivation by stainless steel Cr₂O₃ film.

Material selection: stainless steel 304 vs 316 (Mo for chlorides); Hastelloy and titanium for aggressive service.

Stress corrosion cracking requires tensile stress + corrosive environment (e.g., chlorides on austenitic SS).

Hydrogen embrittlement from H₂S or cathodic charging; use low-hardness steels.

Temperature limits: carbon steel to ~425 °C; creep becomes significant above ~0.4 T_m.

Rate law: −r_A = k C_A^a C_B^b; overall order = a + b.

Elementary reactions follow stoichiometric coefficients as orders; non-elementary need experimental determination.

Half-life first order t_1/2 = ln2/k independent of C_A0; second order t_1/2 = 1/(k C_A0).

Catalyst deactivation: coking, poisoning, sintering; activity a(t) = k(t)/k(0).

Langmuir–Hinshelwood: rate = k K_A P_A/(1 + K_A P_A + K_B P_B)²; adsorption-limited.

Enzyme kinetics Michaelis–Menten: v = V_max S/(K_m + S).

Temperature effects: Arrhenius plot ln k vs 1/T gives slope −E_a/R.

Reaction equilibrium: K = exp(−ΔG°/RT); temperature dependence via van't Hoff.

Distillation column diameter from flooding velocity; Souders–Brown correlation: u = K √((ρ_L − ρ_V)/ρ_V).

Tray efficiency: overall efficiency ≈ 0.5–0.8; Murphree efficiency per tray.

Heat exchanger: TEMA shell-and-tube; shell-side baffles improve heat transfer.

Pressure vessel: hoop stress σ = PD/(2t); longitudinal stress σ = PD/(4t).

Pump selection: centrifugal for high flow/low head; positive displacement for high pressure/low flow.

Compressor: isentropic efficiency; multistage with intercooling reduces work.

Reactor sizing: CSTR vs PFR vs batch; heat transfer area per volume drives reactor choice.

Storage tanks: atmospheric vs pressure vessels; venting and relief requirements.

Temperature: thermocouple (Seebeck), RTD (resistance), thermistor, pyrometer for high temperature.

Pressure: Bourdon tube, diaphragm, strain gauge; differential pressure for flow and level.

Flow: orifice plate, venturi, pitot tube, rotameter, Coriolis and ultrasonic meters.

Level: float, capacitance, ultrasonic, radar, differential pressure.

Composition: gas chromatography, infrared, mass spectrometry, pH electrodes.

Transmitter signal 4–20 mA; zero and span calibration.

Accuracy vs precision; error sources include hysteresis, drift, and nonlinearity.

Control valve sizing uses C_v; cavitation and flashing limits.

Air pollution control: cyclones, baghouses, ESPs, scrubbers; removal efficiency η = (in − out)/in.

Wastewater: primary, secondary (activated sludge), tertiary treatment; BOD/COD ratio indicates biodegradability.

Activated sludge: F/M ratio, SRT, MLSS; nitrification/denitrification for nitrogen removal.

Solid waste hierarchy: reduce, reuse, recycle, recover, dispose.

Greenhouse gases: CO₂, CH₄, N₂O; carbon footprint and life cycle assessment.

Emission limits: permits, NAAQS, and stack testing.

Pollution prevention: source reduction preferred over end-of-pipe treatment.

Sustainability metrics: energy intensity, water use, and waste generation per unit product.

Engineers shall hold paramount the safety, health, and welfare of the public.

Engineers shall perform services only in areas of their competence.

Engineers shall issue public statements only in an objective and truthful manner.

Engineers shall act for each employer or client as faithful agents or trustees; disclose conflicts of interest.

Engineers shall avoid deceptive acts; credit contributions properly.

Engineers shall conduct themselves honorably and report violations to appropriate authority.

Whistleblowing: report imminent danger to public to employer first, then regulatory authority.

Confidentiality: protect proprietary information except when public safety requires disclosure.

Pipe sizing: velocity limits (liquid 1–3 m/s, gas 10–30 m/s) to control erosion and pressure drop.

Fittings: equivalent length method; valves, elbows, tees add to pressure drop.

Pump cavitation: avoid NPSH margin; vapor bubbles collapse causing damage.

Compressors: surge and choke limits; anti-surge control.

Fans and blowers: low pressure rise; centrifugal vs axial.

Piping codes: ASME B31.3 for process piping; hydrostatic testing.

Flow measurement: orifice plate permanent pressure loss; venturi lower loss.

Two-phase flow: flow patterns (slug, annular, bubbly); pressure drop correlations.

Shell-and-tube: tube-side vs shell-side; baffle spacing 0.2–1.0 shell diameter.

Fouling factors: add resistance; cleaning schedule based on fouling rate.

Heat exchanger effectiveness: counterflow > crossflow > parallel.

Boiling: nucleate boiling high h; film boiling low h and dangerous.

Condensers: film condensation; dropwise higher h but unstable.

Furnaces: radiant and convection sections; tube skin temperature limits.

Reboilers: kettle, thermosiphon, forced circulation; selection based on fouling and viscosity.

Compact exchangers: plate-and-frame for high h and low ΔT.

Distillation: tray vs packed column; HETP for packing.

Absorption: packed tower; height = HTU × NTU.

Extraction: mixer-settler, column; solvent selection.

Drying: rotary, spray, fluidized bed; drying curves.

Crystallization: supersaturation; nucleation and growth.

Membrane: RO, UF, MF; flux and rejection.

Adsorption: breakthrough curves; regeneration.

Leaching: solid-liquid extraction; countercurrent stages.

Reactor types: batch, CSTR, PFR, semi-batch; selection based on kinetics and heat.

Heat management: adiabatic temperature rise; heat exchange area per volume.

Mixing: residence time distribution; dispersion model.

Scale-up: geometric similarity; mixing time and power per volume.

Catalyst: fixed bed, fluidized bed, slurry; pressure drop and mass transfer.

Safety: runaway reactions; emergency relief sizing.

Recycle reactors: improve conversion and selectivity.

Membrane reactors: equilibrium shift.

Control loop: sensor, transmitter, controller, final element.

PID tuning: Ziegler–Nichols, Cohen–Coon, IMC.

Cascade control: fast inner loop, slow outer loop.

Feedforward control: compensate measured disturbance.

Ratio control: maintain ratio of two streams.

Split-range control: one controller to two valves.

Dead time compensation: Smith predictor.

Advanced control: MPC, fuzzy, neural.

Block flow diagram vs process flow diagram (PFD) vs piping and instrumentation diagram (P&ID).

Material and energy balances form the basis of design.

Process synthesis: reaction path, separation sequence, heat recovery.

Pinch analysis: minimum utility targets; composite curves.

Heat exchanger network: minimum approach temperature.

Safety: inherent safety in design.

Environmental: emissions and waste minimization.

Economics: capital and operating cost estimation.

Project phases: conceptual, feasibility, detailed design, construction, commissioning.

Gantt chart and critical path method.

Cost estimation: factorial, Lang factor, percentage of delivered equipment.

Risk management: identify, assess, mitigate.

Contracts: lump sum, cost plus, unit price.

Schedule: milestones and float.

Quality: QA/QC.

Stakeholder management.

Hazard identification: HAZOP, what-if, checklist.

Risk assessment: likelihood × severity.

Fire and explosion: flammability limits, flash point.

Toxicology: exposure limits, dose-response.

Personal protective equipment.

Emergency response: evacuation, spill control.

Environmental: air, water, waste.

Regulations: OSHA, EPA.

Public safety paramount.

Competence.

Truthful public statements.

Confidentiality.

Conflict of interest disclosure.

Report violations.

Credit contributions.

Professional development.

Linear regression: y = a + bx; R².

Probability distributions: normal, binomial, Poisson.

Hypothesis testing: t-test, chi-square.

Design of experiments: factorial, response surface.

Optimization: linear programming, nonlinear.

Numerical integration: trapezoid, Simpson.

ODE solution: Euler, RK4.

PDE: finite difference.

Recycle and purge.

Bypass.

Combustion calculations.

Humidification.

Drying.

Crystallization.

Distillation material balance.

Energy integration.

Equations of state: ideal gas, van der Waals, Peng-Robinson.

Activity coefficients.

Vapor-liquid equilibrium.

Chemical equilibrium.

Phase diagrams.

Refrigeration cycles.

Power cycles.

Thermodynamic properties.

Pipe flow.

Packed beds.

Fluidization.

Mixing.

Pumping.

Compression.

Flow measurement.

Two-phase flow.

Conduction.

Convection.

Radiation.

Heat exchangers.

Boiling and condensation.

Furnaces.

Insulation.

Heat integration.

Distillation.

Absorption.

Extraction.

Drying.

Adsorption.

Membranes.

Crystallization.

Leaching.

Batch reactor.

CSTR.

PFR.

Catalysis.

Multiple reactions.

Non-isothermal.

Residence time distribution.

Scale-up.

PID tuning.

Cascade.

Feedforward.

Ratio.

Split-range.

Dead time.

Advanced control.

Safety interlocks.

Flowsheet synthesis.

Pinch analysis.

Equipment selection.

Safety in design.

Environmental design.

Cost estimation.

Optimization.

Debottlenecking.

NPV.

IRR.

Payback.

Break-even.

Sensitivity.

Cost of capital.

Depreciation.

Profitability.

HAZOP.

LOPA.

Fault tree.

Event tree.

Consequence modeling.

Inherent safety.

Emergency planning.

Regulatory compliance.

Whistleblowing.

Conflict of interest.

Confidentiality.

Competence.

Public safety.

Truthful reporting.

Professional development.

Mentoring.