Calculations

Calculations

• 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

  • CadCraft
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  64-bit

• 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

  • CadCraft
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  64-bit

• 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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  64-bit

• 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

  • CadCraft
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  64-bit

• 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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  64-bit

• CSV export of the results

  The results table as comma-separated text.

  Calculator results and export process/calc.js

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  64-bit

• 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

  • CadCraft
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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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

  • CadCraft
  • BimCraft
  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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

  • CadCraft
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  64-bit

• 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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  64-bit

• 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

  • CadCraft
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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• 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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  64-bit

• Stoichiometric matrix

  The 8 by 13 table of how much of each component each process makes or uses.

  Activated sludge plant steady state (ASM1) process/env/water.js

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  64-bit

• Process rates

  The rate of each of the 8 biological processes at given concentrations.

  r₁ = µH × SS ÷ (KS + SS) × SO ÷ (KOH + SO) × XBH (and seven more Monod products)

  Activated sludge plant steady state (ASM1) process/env/water.js

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• Reaction rate of each component

  The net production of each of the 13 components from the 8 process rates.

  dcₖ/dt = Σⱼ νⱼₖ × ρⱼ

  Activated sludge plant steady state (ASM1) process/env/water.js

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  64-bit

• Clarifier split

  The effluent and underflow concentrations from the clarifier feed and the capture fraction a person gives.

  eff = (1 − capture) × c; und = (Qc × c − Qe × eff) ÷ Qu

  Activated sludge plant steady state (ASM1) process/env/water.js

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  64-bit

• Tank mass balances

  The rate of change of every component in every tank: flow in and out, reaction and aeration.

  dc/dt = (Σ Q_in × c_in − Q × c) ÷ V + Σⱼ νⱼ × ρⱼ + KLa × (SO_sat − SO)

  Activated sludge plant steady state (ASM1) process/env/water.js

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  64-bit

• Steady-state iteration

  Advances the plant state with implicit steps until nothing changes any more.

  (I ÷ h − J) × Δy = F(y); stop when max |Fᵢ| ÷ (|yᵢ| + 1) < tol

  Activated sludge plant steady state (ASM1) process/env/water.js

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  64-bit

• COD, nitrogen and oxygen balances, sludge age

  Checks that what enters the plant equals what leaves plus what reacts, and gives the sludge retention time.

  residual = in − out + reaction; rel = residual ÷ (|in| + 10⁻¹²); SRT = Σ V × solids ÷ (Qw × Xw + Qe × Xe)

  Activated sludge plant steady state (ASM1) process/env/water.js

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  64-bit

• Oxygen used and supplied

  The oxygen the reactions use next to what the aerators supply, in kg per day.

  kg/d = g/d ÷ 1000

  Activated sludge plant steady state (ASM1) process/env/water.js

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  64-bit

• Bar-screen head loss

  The head lost through a bar screen.

  h = β × (w ÷ b)^(4/3) × v² ÷ 2g × sin θ

  Water treatment unit processes and sludge sizing process/env/water.js

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  64-bit

• Ideal settling basin

  The overflow rate and the fraction of particles removed.

  v₀ = Q ÷ A; removal = min(1, vs ÷ v₀)

  Water treatment unit processes and sludge sizing process/env/water.js

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  64-bit

• Granular filter head loss

  The head lost through a clean filter bed in laminar flow.

  h = 180 × L × ν × (1 − ε)² × v ÷ (g × ε³ × d²)

  Water treatment unit processes and sludge sizing process/env/water.js

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  64-bit

• Disinfection survival

  The fraction of organisms surviving a contact time, and the log removal.

  s = exp(−k × Cⁿ × t); log removal = −log₁₀(s)

  Water treatment unit processes and sludge sizing process/env/water.js

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• Contact time for a log removal

  The contact time needed to reach a wanted log removal.

  t = log₁₀ removal × ln 10 ÷ (k × Cⁿ)

  Water treatment unit processes and sludge sizing process/env/water.js

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• Sludge retention time

  The mass of sludge in the system divided by the mass leaving per day.

  SRT = V × X ÷ (Qw × Xw + Qe × Xe)

  Water treatment unit processes and sludge sizing process/env/water.js

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  64-bit