Economics & sizing¶

Differentiable equipment sizing, purchased- and bare-module costing, utility costs, and profitability metrics (total annual cost, net present value). Because the correlations are differentiable, capital and operating cost can enter an objective directly.

See the optimization, design & economics guide for worked examples.

economics ¶

Differentiable equipment sizing, capital/operating costing, and economics.

To optimize a process you need an objective with units of money, and that means sizing equipment and costing it. This module supplies smooth, differentiable correlations for both, so a total-annual-cost or net-present-value objective plugs straight into the gradient-based optimizers in fugacio.sim.optimize: you can take the derivative of installed cost with respect to a reflux ratio or a heat-exchanger approach temperature.

Sizing¶

Physically-grounded sizing from process quantities: heat-exchanger area from duty and a log-mean temperature difference, column diameter from the Souders-Brown flooding velocity, vessel volume from a residence time, and so on.

Costing¶

The Turton correlations (Turton et al., Analysis, Synthesis and Design of Chemical Processes) for purchased and bare-module cost:

purchased cost log10 Cp0 = K1 + K2 log10 A + K3 (log10 A)^2 in the size attribute A;
a pressure factor log10 F_P = C1 + C2 log10 P + C3 (log10 P)^2;
the bare-module cost C_BM = Cp0 (B1 + B2 F_M F_P) with a material factor F_M;
escalation from the correlation basis (CEPCI 397, year 2001) to a target CEPCI.

These are smooth in the size and pressure, hence differentiable. The bundled coefficients are representative textbook values for screening-level estimates, not a substitute for a vendor quote.

Operating cost & finance¶

Utility pricing on an energy basis, the capital-recovery factor, total annual cost, net present value, and discounted payback, all differentiable.

Classes:

Name	Description
`EquipmentCost`	Costed equipment item.
`Utility`	A priced utility on an energy basis.

Functions:

Name	Description
`lmtd`	Log-mean temperature difference of the two terminal approaches.
`heat_exchanger_area`	Required heat-transfer area `A = \|Q\| / (U * LMTD)` (m^2).
`vapor_molar_volume_ideal`	Ideal-gas molar volume `V = R T / P` (m^3/mol), a sizing convenience.
`column_diameter`	Column (or knock-out drum) diameter from the Souders-Brown flooding velocity.
`column_height`	Tangent-to-tangent column height from the stage count and tray spacing (m).
`vessel_volume`	Vessel volume from a volumetric flow and liquid residence time (m^3).
`cylinder_volume`	Volume of a vertical cylinder (m^3), a column shell from its size.
`purchased_cost`	Purchased equipment cost `Cp0` at the correlation basis (CEPCI 397), in $.
`pressure_factor`	Turton pressure factor `F_P` (>= 1) for the equipment at gauge pressure (barg).
`bare_module_cost`	Installed (bare-module) cost `C_BM` escalated to the target CEPCI.
`utility_cost`	Annual cost of a utility duty ($/yr) from its energy price.
`capital_recovery_factor`	Capital-recovery factor `i(1+i)^n / ((1+i)^n - 1)` for interest `i` over `n` years.
`annualized_capital`	Annualized capital charge `CRF * CAPEX` ($/yr).
`total_annual_cost`	Total annual cost `TAC = CRF * CAPEX + OPEX` ($/yr), the screening objective.
`npv`	Net present value of a cash-flow stream (index 0 is now), discounted at `rate`.
`discounted_payback`	Discounted payback period (years) for a uniform annual cash inflow.
`installed_capital`	Total installed capital from a list of costed items (optionally Lang-scaled).

EquipmentCost ¶

Bases: NamedTuple

Costed equipment item.

Attributes:

Name	Type	Description
`kind`	`str`	Equipment kind (key into the Turton table).
`size`	`Array`	The sizing attribute used (area m^2, power kW, or volume m^3).
`purchased`	`Array`	Purchased cost `Cp0` escalated to the target CEPCI ($).
`bare_module`	`Array`	Installed bare-module cost `C_BM` ($).

Utility `dataclass` ¶

Utility(name: str, price_per_gj: float)

A priced utility on an energy basis.

Attributes:

Name	Type	Description
`name`	`str`	Utility name.
`price_per_gj`	`float`	Price ($/GJ of heating or cooling delivered).

lmtd ¶

lmtd(dt1: ArrayLike, dt2: ArrayLike) -> Array

Log-mean temperature difference of the two terminal approaches.

Smooth everywhere for positive approaches: as dt1 -> dt2 the value tends to their common limit, with a series expansion used near equality so the gradient stays finite.

heat_exchanger_area ¶

heat_exchanger_area(
    duty: ArrayLike,
    u: ArrayLike,
    dt_hot: ArrayLike,
    dt_cold: ArrayLike,
) -> Array

Required heat-transfer area A = |Q| / (U * LMTD) (m^2).

Parameters:

Name	Type	Description	Default
`duty`	`ArrayLike`	Heat duty `Q` (W); the magnitude is used.	required
`u`	`ArrayLike`	Overall heat-transfer coefficient (W/m^2/K).	required
`dt_hot`	`ArrayLike`	Terminal temperature approach at the hot end (K).	required
`dt_cold`	`ArrayLike`	Terminal temperature approach at the cold end (K).	required

vapor_molar_volume_ideal ¶

vapor_molar_volume_ideal(
    t: ArrayLike, p: ArrayLike
) -> Array

Ideal-gas molar volume V = R T / P (m^3/mol), a sizing convenience.

column_diameter ¶

column_diameter(
    vapor_molar_flow: ArrayLike,
    vapor_density: ArrayLike,
    liquid_density: ArrayLike,
    *,
    molar_mass: ArrayLike = 0.05,
    k_drum: ArrayLike = 0.07,
    flooding: ArrayLike = 0.8,
) -> Array

Column (or knock-out drum) diameter from the Souders-Brown flooding velocity.

The maximum vapour velocity is u_max = k sqrt((rho_L - rho_V)/rho_V); the diameter follows from the volumetric vapour load at the design fraction of flooding.

Parameters:

Name	Type	Description	Default
`vapor_molar_flow`	`ArrayLike`	Vapour molar flow (mol/s).	required
`vapor_density`	`ArrayLike`	Vapour mass density (kg/m^3).	required
`liquid_density`	`ArrayLike`	Liquid mass density (kg/m^3).	required
`molar_mass`	`ArrayLike`	Vapour molar mass (kg/mol) to convert molar to mass flow.	`0.05`
`k_drum`	`ArrayLike`	Souders-Brown coefficient (m/s).	`0.07`
`flooding`	`ArrayLike`	Design fraction of the flooding velocity.	`0.8`

Returns:

Type	Description
`Array`	Diameter (m).

column_height ¶

column_height(
    n_stages: ArrayLike,
    *,
    tray_spacing: ArrayLike = 0.6,
    extra: ArrayLike = 4.0,
) -> Array

Tangent-to-tangent column height from the stage count and tray spacing (m).

vessel_volume ¶

vessel_volume(
    volumetric_flow: ArrayLike,
    *,
    residence_time: ArrayLike = 300.0,
    fill: ArrayLike = 0.5,
) -> Array

Vessel volume from a volumetric flow and liquid residence time (m^3).

cylinder_volume ¶

cylinder_volume(
    diameter: ArrayLike, height: ArrayLike
) -> Array

Volume of a vertical cylinder (m^3), a column shell from its size.

purchased_cost ¶

purchased_cost(kind: str, size: ArrayLike) -> Array

Purchased equipment cost Cp0 at the correlation basis (CEPCI 397), in $.

Uses log10 Cp0 = K1 + K2 log10 A + K3 (log10 A)^2 with A the equipment's capacity attribute (see _TURTON). The size is clipped to the correlation's validity range before the (smooth) evaluation.

pressure_factor ¶

pressure_factor(
    kind: str, pressure_barg: ArrayLike
) -> Array

Turton pressure factor F_P (>= 1) for the equipment at gauge pressure (barg).

bare_module_cost ¶

bare_module_cost(
    kind: str,
    size: ArrayLike,
    *,
    pressure_barg: ArrayLike = 0.0,
    material: str = "CS",
    cepci: ArrayLike = CEPCI_DEFAULT,
) -> EquipmentCost

Installed (bare-module) cost C_BM escalated to the target CEPCI.

C_BM = Cp0 (B1 + B2 F_M F_P) with a material factor F_M and pressure factor F_P, all escalated by cepci / CEPCI_REF.

Parameters:

Name	Type	Description	Default
`kind`	`str`	Equipment kind (key in the Turton table).	required
`size`	`ArrayLike`	Capacity attribute (area m^2, power kW, or volume m^3).	required
`pressure_barg`	`ArrayLike`	Design gauge pressure (barg) for the pressure factor.	`0.0`
`material`	`str`	Material-of-construction key (`"CS"`, `"SS"`, ...).	`'CS'`
`cepci`	`ArrayLike`	Target cost index.	`CEPCI_DEFAULT`

Returns:

Type	Description
`EquipmentCost`	An `EquipmentCost`.

utility_cost ¶

utility_cost(
    duty_w: ArrayLike,
    kind: str,
    *,
    hours_per_year: ArrayLike = HOURS_PER_YEAR,
) -> Array

Annual cost of a utility duty ($/yr) from its energy price.

Parameters:

Name	Type	Description	Default
`duty_w`	`ArrayLike`	Duty (W); the magnitude is used (heating or cooling alike).	required
`kind`	`str`	Utility key in `UTILITIES`.	required
`hours_per_year`	`ArrayLike`	Operating hours per year.	`HOURS_PER_YEAR`

capital_recovery_factor ¶

capital_recovery_factor(
    rate: ArrayLike, years: ArrayLike
) -> Array

Capital-recovery factor i(1+i)^n / ((1+i)^n - 1) for interest i over n years.

annualized_capital ¶

annualized_capital(
    capex: ArrayLike,
    *,
    rate: ArrayLike = 0.1,
    years: ArrayLike = 10.0,
) -> Array

Annualized capital charge CRF * CAPEX ($/yr).

total_annual_cost ¶

total_annual_cost(
    capex: ArrayLike,
    opex: ArrayLike,
    *,
    rate: ArrayLike = 0.1,
    years: ArrayLike = 10.0,
) -> Array

Total annual cost TAC = CRF * CAPEX + OPEX ($/yr), the screening objective.

npv ¶

npv(cash_flows: Array, *, rate: ArrayLike = 0.1) -> Array

Net present value of a cash-flow stream (index 0 is now), discounted at rate.

discounted_payback ¶

discounted_payback(
    capex: ArrayLike,
    annual_cash: ArrayLike,
    *,
    rate: ArrayLike = 0.1,
) -> Array

Discounted payback period (years) for a uniform annual cash inflow.

Solves CAPEX = annual_cash * (1 - (1+i)^-n) / i for n in closed form; smooth and differentiable in all arguments.

installed_capital ¶

installed_capital(
    items: list[EquipmentCost],
    *,
    lang_factor: ArrayLike = 1.0,
) -> Array

Total installed capital from a list of costed items (optionally Lang-scaled).

Economics & sizing¶

economics ¶

Sizing¶

Costing¶

Operating cost & finance¶

EquipmentCost ¶

Utility dataclass ¶

lmtd ¶

heat_exchanger_area ¶

vapor_molar_volume_ideal ¶

column_diameter ¶

column_height ¶

vessel_volume ¶

cylinder_volume ¶

purchased_cost ¶

pressure_factor ¶

bare_module_cost ¶

utility_cost ¶

capital_recovery_factor ¶

annualized_capital ¶

total_annual_cost ¶

npv ¶

discounted_payback ¶

installed_capital ¶

Utility `dataclass` ¶