Calculations

Calculations

• Feed stream

  A feed's total flow and mole fractions from component flows, mass flows or a total with fractions.

  F = Σ nᵢ; zᵢ = nᵢ ÷ F; from mass: nᵢ = mᵢ ÷ Mᵢ

  Flowsheet solver and unit operations process/stream.js

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• Mass flow of a stream

  The mass flow in kg/s from the molar flow and composition.

  ṁ = F × Σ zᵢ Mᵢ

  Flowsheet solver and unit operations process/stream.js

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• Volume flow of a stream

  The volume flow in m³/s, phase by phase.

  Q = Σ_phases F × fraction × V_molar(T, P, x)

  Flowsheet solver and unit operations process/stream.js

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• Mixer

  The outlet of several streams mixed at the lowest inlet pressure.

  nᵢ = Σ F zᵢ; H_flow = Σ F H; outlet from a flash at that enthalpy

  Flowsheet solver and unit operations process/stream.js

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• Splitter

  Outlets that share one stream by given fractions.

  F_k = F × f_k ÷ Σ f

  Flowsheet solver and unit operations process/stream.js

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• Pump

  The shaft work and outlet state of a pump.

  w = V_liquid (P_out − P_in) ÷ η; W = F w; outlet at H_in + w

  Flowsheet solver and unit operations process/stream.js

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• Compressor and expander

  The work and outlet state from an isentropic step and an efficiency.

  h_s from a flash at P_out and the inlet entropy; compressor: h = H_in + (h_s − H_in) ÷ η; expander: h = H_in + η (h_s − H_in)

  Flowsheet solver and unit operations process/stream.js

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• Component splitter

  Two outlets that each take a set fraction of every component.

  aᵢ = F zᵢ fᵢ; bᵢ = F zᵢ (1 − fᵢ); Q = F_a H_a + F_b H_b − F H

  Flowsheet solver and unit operations process/stream.js

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• Two-stream heat exchanger

  The outlet states, duty, log-mean temperature difference, UA and smallest approach of a counter-current exchanger.

  duty = F_hot (H_in − H_out); LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁ ÷ ΔT₂), or ΔT₁ when |ΔT₁ − ΔT₂| < 1e-9; UA = duty ÷ LMTD

  Flowsheet solver and unit operations process/stream.js

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• Inside diameter of a pipe size

  The inside diameter in meters of a nominal pipe size or a size in millimeters.

  D = (OD − 2 × wall) × 0.0254 (inches from the schedule 40 table); D = mm ÷ 1000

  Line sizing and pressure drop process/hydraulics.js

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• Colebrook–White friction factor

  The turbulent Darcy friction factor from the implicit Colebrook–White equation.

  1 ÷ √f = −2 log₁₀(ε ÷ (3.7D) + 2.51 ÷ (Re √f))

  Line sizing and pressure drop process/hydraulics.js

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• Swamee–Jain friction factor

  The turbulent Darcy friction factor from an explicit formula.

  f = 0.25 ÷ (log₁₀(ε ÷ (3.7D) + 5.74 ÷ Re^0.9))²

  Line sizing and pressure drop process/hydraulics.js

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• Friction factor

  The Darcy friction factor for any Reynolds number.

  Re < 2300: 64 ÷ Re; Re ≥ 4000: Swamee–Jain; between: (1 − w) × 64 ÷ 2300 + w × f(4000), w = (Re − 2300) ÷ 1700

  Line sizing and pressure drop process/hydraulics.js

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• Erosional velocity

  The velocity above which API RP 14E warns of erosion, in m/s.

  v_e = C × 0.3048 ÷ √(ρ × 0.062427961), C = 100

  Line sizing and pressure drop process/hydraulics.js

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• Pressure drop of one line

  Velocity, Reynolds number, friction factor and the friction, fitting and static parts of the pressure drop.

  A = πD² ÷ 4; v = ṁ ÷ (ρA); Re = ρvD ÷ μ; Δp = f (L ÷ D) ρv² ÷ 2 + K ρv² ÷ 2 + ρ g Δz

  Line sizing and pressure drop process/hydraulics.js

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• Fluid of a stream

  The density, mass flow and phase of a solved stream for the line calculation.

  ρ = mass flow ÷ volume flow; gas when vapor fraction ≥ 0.999, liquid when ≤ 0.001, else two-phase

  Line sizing and pressure drop process/hydraulics.js

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• Pipe in a flowsheet

  The outlet pressure of a pipe unit, with the gas density taken at the mean pressure.

  ρ_mean = ρ_in × (P_in + P_out) ÷ 2 ÷ P_in; repeat until |ΔP_out| < 1e-6 P_in

  Line sizing and pressure drop process/hydraulics.js

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• Length, rise and bends of a 3D pipe run

  A pipe run's length and rise in meters and its count of elbows, from its points in millimeters.

  L = Σ |pᵢ − pᵢ₋₁| ÷ 1000; Δz = (z_last − z_first) ÷ 1000; bend angle = acos(a·b ÷ (|a||b|))

  Line sizing and pressure drop process/model.js

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• Hydraulics of every linked line

  The pressure drop, velocity and erosion screening of each stream that has a line or a pipe run.

  Line sizing and pressure drop process/model.js

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• Stream table

  The table of streams drawn on the P&ID and exported: temperature, pressure, flows, velocity, line drop and composition.

  T (°C) = T − 273.15; P (bar) = P ÷ 1e5; mass (kg/h) = ṁ × 3600; rounded with toPrecision to 5, 3 or 4 significant digits

  Line sizing and pressure drop process/model.js

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• Pipe size for a velocity target

  The smallest nominal pipe size whose velocity is at or under the target.

  v = (ṁ ÷ ρ) ÷ (πD² ÷ 4) ≤ v_max, sizes tried from smallest to largest

  Line sizing and pressure drop process/synth.js

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• Rescaling a plant to a production rate

  The factor applied to the feed so a chosen stream carries the asked-for tonnes per day of a component.

  k = (t/d × 1000 ÷ 86400) ÷ (F zᵢ Mᵢ)

  Line sizing and pressure drop process/synth.js

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• Stream segments from enthalpies

  A process stream with phase change as a list of pieces with constant heat capacity flow rate.

  12 equal temperature steps; CP = |F (H_k − H_{k−1}) ÷ (T_k − T_{k−1})|

  Pinch analysis process/pinch.js

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• Problem table

  The minimum hot and cold utility and the pinch temperature for a minimum approach.

  shift hot streams by −ΔT_min⁄2 and cold by +ΔT_min⁄2; net_k = Σ (±CP)(T_hi − T_lo); Q_H = −min of the running sum; Q_C = last running sum + Q_H

  Pinch analysis process/pinch.js

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• Composite curves

  The hot and cold composite curves as lists of enthalpy and temperature points.

  H_{k+1} = H_k + (Σ CP of the streams present) × (T_{k+1} − T_k); cold curve shifted by Q_C

  Pinch analysis process/pinch.js

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• Area target

  The minimum heat-exchange area for the composite curves with vertical heat transfer.

  A = Σ_intervals (Σ_streams CPᵢ ΔTᵢ ÷ hᵢ) ÷ ΔT_lm, ΔT_lm = (d₀ − d₁) ÷ ln(d₀ ÷ d₁)

  Pinch analysis process/pinch.js

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• Minimum number of units

  The fewest exchangers, heaters and coolers for maximum energy recovery.

  above the pinch: streams + (1 if Q_H > 1e-9) − 1; below: streams + (1 if Q_C > 1e-9) − 1

  Pinch analysis process/pinch.js

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• Purchased cost of one item

  The purchased cost of an equipment item of a given size, in base-year dollars or scaled by a cost index.

  C₀ = 10^(K₁ + K₂ log₁₀ A + K₃ (log₁₀ A)²); C = C₀ × I_now ÷ I_base

  Capital and operating cost process/cost.js

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• Six-tenths scaling

  A known cost scaled to another size.

  C₂ = C₁ (A₂ ÷ A₁)^n, n = 0.6 unless given

  Capital and operating cost process/cost.js

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• Installed cost

  The installed plant cost from the purchased equipment total.

  installed = purchased × Lang factor (3.10 solid, 3.63 solid–fluid, 4.74 fluid)

  Capital and operating cost process/cost.js

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• Energy cost

  The cost of energy per hour and per year for a list of powers and prices.

  per hour = Σ |P| ÷ 1000 × price; per year = per hour × hours (8000 unless given)

  Capital and operating cost process/cost.js

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• Equipment cost table

  The cost of every item, the purchased total and the installed total.

  purchased = Σ cost of the rows; installed = purchased × Lang factor

  Capital and operating cost process/cost.js

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• Results table lines

  A result object as a flat list of named values for the calculator's table.

  number → +v.toPrecision(6); list of numbers → count, first and last to 5 digits

  Calculator results and export process/calc.js

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• CSV export of the results

  The results table as comma-separated text.

  Calculator results and export process/calc.js

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• Figure for the status bar

  The yearly emissions, installed cost or campaign length a run adds to the running totals.

  value = Number(the results line with that name)

  Calculator results and export process/calc.js

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• Molecular dynamics set-up

  The lattice spacing, cell count and cutoff of the Lennard-Jones liquid calculator.

  a = ∛(4 ÷ ρ); n = min(max(2 | n_typed, 2), 6); r_c = min(2.5, n a ÷ 2 − 1e-6)

  Calculator results and export process/calc.js

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• Column outlet compositions

  The outlet flows and mole fractions the column calculator lists.

  zᵢ → +zᵢ.toPrecision(5)

  Calculator results and export process/calc4.js

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• Pump power and suction head margin

  The hydraulic power of a pump and the margin between the available and required net positive suction head.

  power = ρ g Q H ÷ η; NPSH_r by straight-line interpolation between the maker's points; margin = NPSH_a − NPSH_r

  Calculator results and export process/calc4.js

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• Mesh energy against the plain sum

  The relative difference between the particle-mesh and plain Ewald reciprocal energies.

  |E_mesh − E_plain| ÷ |E_plain|

  Calculator results and export process/calc4.js

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• Coordinate rounding

  A coordinate or label value rounded for the drawing.

  f(v) = +v.toFixed(3); 0 when v is not finite

  Process diagram entities process/draw.js

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• Stream label

  The text under a stream arrow: its name, temperature in degrees Celsius and pressure in bar.

  T (°C) = T − 273.15; P (bar) = P ÷ 1e5; both to 3 decimals

  Process diagram entities process/draw.js

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• Point inside a node boundary

  Whether a tag or line label lies inside a hazard study node's region.

  count the sides whose ends straddle the point's height and cross to its right; inside when the count is odd

  Process diagram entities process/draw.js

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• Controller faceplate numbers

  The set point, measurement, output and error a controller faceplate shows from a simulation.

  error = set point − last measurement

  Process diagram entities process/draw.js

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• Atomic weights

  The atomic weight of each element the structure reader knows.

  H 1.008; C 12.011; N 14.007; O 15.999; S 32.06; Cl 35.45 …

  Molar mass and group-contribution estimates process/env/cheminfo.js

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• Molar mass

  The molar mass of a molecule in g/mol.

  M = Σ count × atomic weight

  Molar mass and group-contribution estimates process/env/cheminfo.js

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• Joback estimate

  Boiling point, critical temperature, pressure and volume, melting point, formation enthalpy and Gibbs energy, heat capacity and acentric factor of a molecule.

  T_b = 198 + Σ; T_c = T_b ÷ (0.584 + 0.965 Σ − Σ²); P_c = (0.113 + 0.0032 n_atoms − Σ)⁻²; ω = 3⁄7 × θ ÷ (1 − θ) × log₁₀(P_c ÷ 1.01325) − 1, θ = T_b ÷ T_c

  Molar mass and group-contribution estimates process/env/cheminfo.js

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• Component from a structure

  A component for the property package from the Joback estimate, with a quadratic heat-capacity fit.

  C_p ÷ R ≈ A + B T + C T² fitted at 11 temperatures from 300 to 800 K; h_f (J/mol) = H_f (kJ/mol) × 1000

  Molar mass and group-contribution estimates process/env/cheminfo.js

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• Dispersion coefficients

  The crosswind and vertical spread of the plume at a distance downwind, for a stability class and terrain.

  σy = ay·x·(1 + by·x)^ey; σz = az·x·(1 + bz·x)^ez

  Gaussian plume concentration and contours process/env/plume.js

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• Plume concentration at a point

  The concentration at a point downwind, crosswind and above ground from a continuous release.

  C = Q ÷ (2π·u·σy·σz) × exp(−y² ÷ 2σy²) × [exp(−(z − H)² ÷ 2σz²) + exp(−(z + H)² ÷ 2σz²)]

  Gaussian plume concentration and contours process/env/plume.js

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• Reach of a concentration level

  The farthest downwind distance where the ground-level centerline concentration is still at or above an endpoint.

  Gaussian plume concentration and contours process/env/plume.js

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