Calculations

Calculations

• 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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• Half-width of a contour

  Half the crosswind width of a concentration level at a given distance.

  w = σy × √(2 × ln(C₀ ÷ C_end))

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

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• Height of a contour

  The height above ground up to which the concentration stays at or above the endpoint at a given distance.

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

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• Contour polygon in site coordinates

  The outline of a concentration level as a polygon on the site plan, with its reach and greatest height.

  (x, y) → (cx + x·cos t − y·sin t, cy + x·sin t + y·cos t)

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

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• Gas density relative to air

  Whether the released gas is heavier than air, which makes a Gaussian result untrustworthy.

  ratio = (P·M ÷ R·T) ÷ (P·M_air ÷ R·T_air); dense when ratio > 1.1

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

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• Wind speed at height

  The wind speed at a height from the speed measured at 10 m.

  u = u₁₀ × (max(z, 1) ÷ 10)^p

  Stack plume rise and air dispersion screening process/env/dispersion.js

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• Plume rise and effective height

  How far the plume rises above the stack and the effective release height used by the plume equation.

  Fb = g·vs·d²·(Ts − Ta) ÷ 4Ts; Δh = 21.425·Fb^0.75 ÷ u (Fb < 55) or 38.71·Fb^0.6 ÷ u; stable: Δh = 2.6·∛(Fb ÷ u·s)

  Stack plume rise and air dispersion screening process/env/dispersion.js

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• Stack from a flowsheet stream

  Exit velocity, volume flow and the emission rate of each species from a process stream.

  V̇ = F·R·T ÷ P; vs = V̇ ÷ (π·d² ÷ 4); Qᵢ = F·zᵢ·MWᵢ

  Stack plume rise and air dispersion screening process/env/dispersion.js

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• Concentration from one stack at one point

  The ground concentration in µg/m³ from one source for one wind speed and stability class.

  Stack plume rise and air dispersion screening process/env/dispersion.js

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• Worst-case 1-hour concentration

  The highest ground-level concentration over all stability classes, wind speeds and distances, and its longer-period estimates.

  xᵢ = xMin × (xMax ÷ xMin)^(i ÷ steps); C_avg = C_max × factor

  Stack plume rise and air dispersion screening process/env/dispersion.js

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• Receptor position in the wind frame

  The downwind and crosswind distance of a receptor from a source for one hour's wind direction, and the concentration there.

  θ = (dirFrom + 180) mod 360; x_d = dx·sin θ + dy·cos θ; y_c = dx·cos θ − dy·sin θ

  Stack plume rise and air dispersion screening process/env/dispersion.js

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• Hour-by-hour statistics at receptors

  The highest and second-highest hourly value, the period mean and the highest 24-hour mean at each receptor.

  mean = Σ cₕ ÷ n; rolling₂₄ = max over windows of (Σ of 24 hours) ÷ 24

  Stack plume rise and air dispersion screening process/env/dispersion.js

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• Contours for a site plan

  The contour polygon of each concentration level for one wind condition, in site coordinates.

  angle = 90 − ((dirFrom + 180) mod 360); C_end = level × 10⁻⁶

  Stack plume rise and air dispersion screening process/env/dispersion.js

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• Comparison with a limits pack

  Whether a result is above, or within 80 % of, the limit a person typed for that pollutant and averaging time.

  fraction = c ÷ limit

  Stack plume rise and air dispersion screening process/env/dispersion.js

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• Contours as drawing entities

  The contour polylines, stack marker, wind arrow and labels placed in a drawing.

  drawing point = site point × scale

  Stack plume rise and air dispersion screening process/env/plumedraw.js

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