Process Costing Using SSLW Process and Product Design Principles

Introduction

IDAES Process Costing Framework

Note

This document outlines an example process costing library to support IDAES unit models. For a general overview of costing capabilities in IDAES, see the IDAES Process Costing Framework.

Note

Process costing methods are available for most of the unit operations in the IDAES Unit Model Library (Compressor, CSTR, Flash, Heater, HeatExchanger, HeatExchangerNTU, PFR, PressureChanger, Pump, StoichiometricReactor, Turbine, and generic vessels).

A process costing module has been developed primarily based on base cost and purchase cost correlations from the following reference with some exceptions (noted in the documentation as appropriate):

Process and Product Design Principles: Synthesis, Analysis, and Evaluation. Seider, Seader, Lewin, Windagdo, 3rd Ed. John Wiley and Sons. Chapter 22. Cost Accounting and Capital Cost Estimation

This library implements some of the methods described in the source, and outlines capital cost methodology for generic IDAES unit operations. The module employs Pyomo currency units using a basis Chemical Engineering Cost Index value of 500 (USD CE500) - this index creates a relative comparison scale for capital costs betweens years. Users may then pass a desired year (default USD 2018 for the SSLW costing module) and the framework will automatically convert currency units using a built-in dictionary of year/cost index definitions. The base costing framework provides a method to automatically register currency units for the costing block based on Chemical Engineering (CE) Cost Index conversion rates for US Dollars. IDAES will check if Pyomo has standard currency units registered, and if not will load unit conversions between USD at CE indices of 500 and 394, as well as USD annually from 1990 to 2020. Users should refer to the reference above for details of the costing correlations, however, a summary of the methods is provided below.

Available IDAES Process Costing Module Methods

When generating a costing block self.costing for a unit model self (e.g. m.fs.H101.costing), the costing block is automatically populated with the following variables:

Table 1. Main Variables added to the unit block (“self.costing”).

Variable	Symbol	Units	Notes
Purchase cost	\(purchase\_cost\)	dollars	Equipment cost adjusted for pressure, material, length and quantity factors
Base cost per unit	\(base\_cost\_per\_unit\)	unitless	Base cost per unit before adjustment (from costing correlations)
Base cost	\(base\_cost\)	unitless	Base cost of total set of units (base cost per unit * number of units)
Number of units	\(number\_of\_units\)	unitless	Number of units to be costed (to take advantage of the economics of scale)

Note

number of units by default is fixed to 1 and the user must unfix this variable to optimize the number of units. Also, number_of_units can be built as a continuous variable or an integer variable. If the latter, the user must provide a MIP solver. Use the global costing argument for this purpose (integer_n_units=True or False).

For a particular unit model, capital costs are assumed to scale with a selected basis quantity:

Table 2. Cost basis for each unit model

Unit Model	Basis Quantity	Basis Units
heat exchanger	\(area\)	\(ft^2\)
pump	\(fluid_{work}\)	\(ft^3/s\)
compressor	\(mechanical_{work}\)	\(hp\)
turbine	\(mechanical_{work}\)	\(hp\)
vessels	\(D , L\)	\(ft\)
fired heaters	\(heat\_duty\)	\(BTU/hr\)

Example

Below is a example of how to add and solve an SSLW costing block for a flowsheet including a heat exchanger:

from pyomo.environ import ConcreteModel, SolverFactory
from pyomo.util.calc_var_value import calculate_variable_from_constraint
from idaes.core import FlowsheetBlock
from idaes.models.unit_models.heat_exchanger import HeatExchanger, HeatExchangerFlowPattern
from idaes.models.properties import iapws95

from idaes.models.costing.SSLW import SSLWCosting, SSLWCostingData
from idaes.core import UnitModelCostingBlock
from idaes.models.costing.SSLW import HeaterMaterial, HeaterSource

m = ConcreteModel()
m.fs = FlowsheetBlock(dynamic=False)

m.fs.properties = iapws95.Iapws95ParameterBlock()

m.fs.unit = HeatExchanger(
            shell={"property_package": m.fs.properties},
            tube={"property_package": m.fs.properties},
            flow_pattern=HeatExchangerFlowPattern.countercurrent})
# set inputs
m.fs.unit.shell_inlet.flow_mol[0].fix(100)     # mol/s
m.fs.unit.shell_inlet.enth_mol[0].fix(3500)    # j/s
m.fs.unit.shell_inlet.pressure[0].fix(101325)  # Pa

m.fs.unit.tube_inlet.flow_mol[0].fix(100)
m.fs.unit.tube_inlet.enth_mol[0].fix(4000)
m.fs.unit.tube_inlet.pressure[0].fix(101325.0)

m.fs.unit.area.fix(1000)  # m2
m.fs.unit.overall_heat_transfer_coefficient.fix(100)  # W/m2K

m.fs.costing = SSLWCosting()
m.fs.H101.costing = UnitModelCostingBlock(
    flowsheet_costing_block=m.fs.costing,
    costing_method=SSLWCostingData.cost_heat_exchanger,
    costing_method_arguments={
        "hx_type": HXType.Utube,
        "material_type": HXMaterial.StainlessSteelStainlessSteel,
        "tube_length": HXTubeLength.TwelveFoot,
        "integer": True,
    }
)

m.fs.unit.initialize()

opt = SolverFactory('ipopt')
opt.options = {'tol': 1e-6, 'max_iter': 50}
results = opt.solve(m, tee=True)

Unit Mapping

As a convenience for users, common unit models are mapped with appropriate costing methods if no costing method is passed:

Table 2. Mapped costing method for each unit model.

Unit Model	Costing Method
CSTR	cost_vertical_vessel
Compressor	cost_compressor
Flash	cost_vertical_vessel
Heater	cost_fired_heater
HeatExchanger	cost_heat_exchanger
HeatExchangerNTU	cost_heat_exchanger
PFR	cost_horizontal_vessel
PressureChanger	cost_pressure_changer
Pump	cost_pump
StoichiometricReactor	cost_horizontal_vessel
Turbine	cost_turbine

The mapping follows unit model hierarchy (inheritance) and the framework will find the best match among available costing methods. For example, pumps will try costing with cost_pump() and fall back to cost_pressure_changer().

Heat Exchanger Cost

Note

IDAES does not yet support costing for heat exchangers requiring both shell and tube area (HX1D).

The purchase cost is computed based on the base unit cost and three correction factors (Eq. 22.43 in Seider et al.), and is adjusted by user-defined currency units with the appropriate CE index value. The base cost is computed depending on the heat exchanger type selected by the user.

The heat exchanger costing method has three arguments, hx_type = heat exchanger type, material_type = construction material, and tube_length = tube length (‘*’ corresponds to the default options):

• hx_type :

  • ‘floating_head’

  • ‘fixed_head’

  • ‘Utube’*

  • ‘Kettle_vap’

• material_type (shell-tube):

  • ‘CarbonSteelCarbonSteel’

  • ‘CarbonSteelBrass’

  • ‘CarbonSteelStainlessSteel’*

  • ‘CarbonSteelMonel’

  • ‘CarbonSteelTitanium’

  • ‘CarbonSteelCrMoSteel’

  • ‘CrMoSteelCrMoSteel’

  • ‘MonelMonel’

  • ‘TitaniumTitanium’

• tube_length:

  • ‘8ft’

  • ‘12ft’*

  • ‘16ft’

  • ‘20ft’

Additionally, users may pass an argument ‘integer’ (defaults to True`) whether the number of units should be restricted to an integer or not.

\[self.costing.purchase\_cost = pressure\_factor*material\_factor*L\_factor*self.costing.base\_cost\]

\[self.costing.base\_cost\_per\_unit = \exp{(\alpha_{1} - \alpha_{2}*\log{area*hx\_os} + \alpha_{3}*(\log{area*hx\_os})^{2})}\]

\[self.costing.base\_cost = self.costing.base\_cost\_per\_unit * self.costing.number\_of\_units\]

\[area = self.area / self.costing.number\_of\_units\]

where:

• pressure_factor - is the pressure design correction factor

• material_factor - is the construction material correction factor

• length_factor - is the tube length correction factor

• hx_os - heat exchanger oversize factor (default = 1)

• area - heat exchanger area

Table 3. Base cost factors for heat exchanger type.

HX Type	\(\alpha_{1}\)	\(\alpha_{2}\)	\(\alpha_{3}\)
floating_head	11.9052	0.8709	0.09005
fixed_head	11.2927	0.8228	0.09861
Utube	11.3852	0.9186	0.09790
Kettle_vap	12.2052	0.8709	0.09005

Table 4. Tube-Length correction factor.

HX Tube Length (ft)	FL
8	1.25
12	1.12
16	1.05
20	1.00

Construction material correction factor (FM_Mat) can be computed with Eq. 22.44 (Seider et al.)

\[material\_factor = a + (\frac{area}{100})^{b}\]

Table 5. Materials of construction factors.

Materials of Construction
Shell / Tube	a	b
carbon steel/carbon steel	0.00	0.00
carbon steel/brass	1.08	0.05
carbon steel/stainless steel	1.75	0.13
carbon steel/monel	2.1	0.13
carbon steel/titanium	5.2	0.16
carbon steel/Cr-Mo steel	1.55	0.05
Cr-Mo steel/Cr-Mo steel	1.7	0.07
stainless steel/stainless steel	2.7	0.07
monel/monel	3.3	0.08
titanium/titanium	9.6	0.06

Pressure Changer Cost

The costing of a pressure changer unit model is more complicated, because the pressure changer model can be imported into the flowsheet object representing a pump, turbine, compressor, or a simple pressure changer (fan, blower, etc.). The cost_pressure_changer method currently supports costing of pumps, turbines, and compressors. The method automatically interrogates the flowsheet object to determine if the unit is being used as a pump, turbine, or compressor.

The cost_pressure_changer() method authomatically determines if the unit model is being used as a pump, turbine, or compressor based on the compressor and thermodynamic_assumption configuration arguments provided by the user where creating the unit model. A summary of the decision logic is shown below.

Unit Type	compressor	thermodynamic_assumption
Turbine	False	Any
Pump	True	pump
Mover	True	not pump, isothermal or adiabatic

Additionally, some unit types have different sub-types which can be costed appropriately. In these cases, an additional argument is provided to cost_pressure_changer to identify the sub-type to use which is detailed below.

Turbine Cost Model

The turbine cost is based on the mechanical work of unit (work_mechanical), this correlation has been obtained using the NETL Report (DOE/NETL 2015).

\[self.costing.purchase\_cost = 530*(mechanical_{work})^{0.81}\]

DOE/NETL, 2015, report. Cost and performance Baseline for Fossil Energy Plants. Volume 1a: Bituminous Coal (PC) and Natural Gas to Electricity. Revision 3

Users may pass an argument ‘integer’ (defaults to True) whether the number of units should be restricted to an integer or not.

Pump Cost Model

Three subtypes are supported for costing of pumps, which can be set using the “pump_type” argument (‘*’ corresponds to the default options):

1. Centrifugal pumps (pump_type=’Centrifugal’)*

2. External gear pumps (pump_type=’ExternalGear’)

3. Reciprocating Plunger pumps (pump_type=’Reciprocating’)

Additionally, there are an array of additional pump options:

• material_type:

  • ‘CastIron’

  • ‘DuctileIron’

  • ‘CastSteel’

  • ‘Bronze’

  • ‘StainlessSteel’*

  • ‘HastelloyC’

  • ‘Monel’

  • ‘Nickel’

  • ‘Titanium’

  • ‘NiAlBronze’

  • ‘CarbonSteel’

Additionally, users may pass an argument ‘integer’ (defaults to True) whether the number of units should be restricted to an integer or not.

Centrifugal Pump

The centrifugal pump cost has two main components, the cost of the pump and the cost of the motor. The pump cost is based on the fluid work (work_fluid), pump head, and size factor.

Additional arguments are required (‘*’ corresponds to the default options):

• pump_type_factor (empirical factor, see table 6):

  • 1.1

  • 1.2

  • 1.3

  • 1.4*

  • 2.1

  • 2.2

• pump_motor_type_factor:

  • ‘open’*

  • ‘enclosed’

  • ‘explosion_proof’

In the lists above, * marks the default options.

Based on user’s inputs the costing method builds base_cost and purchase_cost for both the pump and the motor. The unit purchase cost is obtained by adding the motor and pump costs.

\[self.costing.purchase\_cost = self.costing.pump\_purchase\_cost + self.costing.motor\_purchase\_cost\]

To compute the purchase cost of the centrifugal pump, first we obtain the pump size factor (S) with Eq. 22.13, then we obtain the base cost with Eq. 22.14. Finally, the purchase cost of the pump is obtained in Eq. 22.15. (Seider et al.) and is adjusted by user-defined currency units with the appropriate CE index value.

\[S = QH^{0.5}\]

\[self.costing.pump\_base\_cost\_per\_unit = \exp{(9.7171 - 0.6019*\log{S} + 0.0519*(\log{S})^{2})}\]

\[self.costing.pump\_purchase\_cost = F_{T}*material\_factor*self.costing.pump\_base\_cost\]

\[self.costing.base\_cost = self.costing.pump\_base\_cost\_per\_unit * self.costing.number\_of\_units\]

\[Q = self.Q / self.costing.number\_of\_units\]

Note

the same number of units have been considered for pumps and the pump motor

where:

• S is the pump size factor (self.costing.size_factor)

• Q is the volumetric flowrate in gpm (depending on the model this variable can be found as self.unit.properties_in.flow_vol)

• H is the head of the pump in ft (self.pump_head; which is defined as \(H = \Delta P/\rho_{liq}\))

• FT is a parameter fixed based on the pump_type_factor argument (users must wisely select this factor based on the pump size factor, pump head range, and maximum motor hp)

• material_factor is the material factor for the pump

Table 6. Pump Type factor (Table 22.20 in Seider et al.).

Case	FT factor	# stages	Shaft rpm	Case-split	Pump Head range (ft)	Maximum Motor Hp
‘1.1’	1.00	1	3600	VSC	50 - 900	75
‘1.2’	1.50	1	1800	VSC	50 - 3500	200
‘1.3’	1.70	1	3600	HSC	100 - 1500	150
‘1.4’	2.00	1	1800	HSC	250 - 5000	250
‘2.1’	2.70	2	3600	HSC	50 - 1100	250
‘2.2’	8.90	2+	3600	HSC	100 - 1500	1450

For more details on how to select the FT factor, please see Seider et al.

Table 7. Materials of construction factors for centrifugal pumps and external gear pumps.

Material Factor	FM_MAT
cast iron	1.00
ductile iron	1.15
cast steel	1.35
bronze	1.90
stainless steel	2.00
hastelloy C	2.95
monel	3.30
nickel	3.50
titanium	9.70

Electric Motor Pumps

A centrifugal pump is usually driven by an electric motor, the self.costing.motor_purchase_cost is calculated based on the power consumption and is adjusted by user-defined currency units with the appropriate CE index value.

\[self.costing.motor\_purchase\_cost = FT * self.costing.motor\_base\_cost (Eq. 22.20)\]

\[self.costing.motor\_base\_cost = self.costing.motor\_base\_cost\_per\_unit * self.costing.number\_of\_units\]

\[Q = self.Q / self.costing.number\_of\_units\]

\[\begin{split}self.costing.motor\_base\_cost\_per\_unit = e^{(5.8259 + 0.13141\log{PC} + \\ 0.053255(\log{PC})^{2} + 0.028628(\log{PC})^{3} - 0.0035549(\log{PC})^{4})} (Eq. 22.19)\end{split}\]

\[PC = \frac{P_{T}}{\eta_{P}\eta_{M}} = \frac{P_{B}}{\eta_{M}} = \frac{Q H \rho}{33000\eta_{P}\eta_{M}} (Eq. 22.16)\]

\[\eta_{P} = -0.316 + 0.24015*\log{Q} - 0.01199(\log{Q})^{2} (Eq. 22.17)\]

\[\eta_{M} = 0.80 + 0.0319\log{PB} - 0.00182(\log{PB})^{2} (Eq. 22.18)\]

Efficiencies are valid for PB in the range of 1 to 1500 Hp and Q in the range of 50 to 5000 gpm

where:

• motor_FT is the motor type correction factor

• PC is the power consumption in hp (self.power_consumption_hp; coded as a pyomo expression)

• Q is the volumetric flowrate in gpm (self.Q_gpm)

• H is the pump head in ft (self.pump_head)

• PB is the pump brake hp (self.work)

• nP is the fractional efficiency of the pump

• nM is the fractional efficiency of the motor

• \(\rho\) is the liquid density in lb/gal

Table 8. FT Factors in Eq.(22.20) and Ranges for electric motors.

Type Motor Enclosure	3600rpm	1800rpm
Open, drip-proof enclosure, 1 to 700Hp	1.0	0.90
Totally enclosed, fan-cooled, 1 to 250Hp	1.4	1.3
Explosion-proof enclosure, 1 to 25Hp	1.8	1.7

External Gear Pumps

External gear pumps are not as common as the contrifugal pump, and various methods can be used to correlate base cost. Eq. 22.21 in Seider et al. Here the purchase cost is computed as a function of the volumetric flowrate (Q) in gpm Eq. 22.22 in Seider et al. and is adjusted by user-defined currency units with the appropriate CE index value.

\[self.costing.pump\_purchase\_cost = material\_factor * self.costing.pump\_base\_cost\]

\[self.costing.pump\_base\_cost = self.costing.pump\_base\_cost\_per\_unit * self.costing.number\_of\_units\]

\[self.costing.self.costing.pump\_base\_cost\_per\_unit = \exp{(7.6964 + 0.1986\log{Q} + 0.0291(\log{Q})^{2})}\]

\[Q = self.Q / self.costing.number\_of\_units\]

Reciprocating Plunger Pumps

The cost correlation method used here is based on the brake horsepower (PB) and is adjusted by user-defined currency units with the appropriate CE index value.

\[self.costing.pump\_purchase\_cost = material\_factor * self.costing.pump\_base\_cost (Eq. 22.22)\]

\[self.costing.pump\_base\_cost = self.costing.pump\_base\_cost\_per\_unit * self.costing.number\_of\_units\]

\[self.costing.pump\_base\_cost\_per\_unit = \exp{(7.8103 + 0.26986\log{PB} + 0.06718(\log{PB})^{2})} (Eq. 22.23)\]

\[PB = f(Q)\]

\[Q = self.Q / self.costing.number\_of\_units\]

Table 9. Materials of construction factors for reciprocating plunger pumps.

Material	Mat_factor
ductile iron	1.00
Ni-Al-Bronze	1.15
carbon steel	1.50
stainless steel	2.20

Mover (Compressor, Fan, Blower)

If the unit represents a “Mover”, the user can select to cost it as a compressor, fan, or blower.

Therefore, the user must set the “mover_type” argument (‘*’ corresponds to the default options):

• mover_type (upper/lower case sensitive):

  • ‘compressor’*

  • ‘fan’

  • ‘blower’

Compressor Cost

The compressor cost is based on the mechanical work of the unit and is adjusted by user-defined currency units with the appropriate CE index value.

Additional arguments are required to estimate the cost such as compressor type, driver mover type, and materials of construction (‘*’ corresponds to the default options):

• compressor_type:

  • ‘Centrifugal’*

  • ‘Reciprocating’

  • ‘Screw’

• driver_mover_type:

  • ‘ElectricMotor’*

  • ‘SteamTurbine’

  • ‘GasTurbine’

• material_type:

  • ‘CarbonSteel’

  • StainlessSteel’*

  • ‘NickelAlloy’

Additionally, users may pass an argument ‘integer’ (defaults to True) whether the number of units should be restricted to an integer or not.

\[self.costing.purchase\_cost = F_{D} * material\_factor * self.costing.base\_cost\]

\[self.costing.base\_cost = self.costing.base\_cost\_per\_unit * self.costing.number\_of\_units\]

\[self.costing.base\_cost\_per\_unit = \exp{(\alpha_{1} + \alpha_{2}*\log{mechanical_{work}})}\]

\[mechanical_{work} = self.mechanical_{work} / self.costing.number\_of\_units\]

where:

• FD is the driver mover type factor and FM is the construction material factor.

Table 10. Compressor type factors.

Compressor type	\(\alpha_{1}\)	\(\alpha_{2}\)
Centrifugal	7.5800	0.80
Reciprocating	7.9661	0.80
Screw Compressor	8.1238	0.7243

Table 11. Driver mover type (for compressors only).

Mover type	FD (mover_type)
Electric Mover	1.00
Steam Turbine	1.15
Gas Turbine	1.25

Table 12. Material of construction factor (for compressors only).

Material	Mat_factor
Cast iron	1.00
Stainless steel	1.15
Nickel alloy	1.25

Fan Cost

The fan cost is a function of the actual cubic feet per minute (Q) entering the fan.

Additional arguments are required to estimate the fan cost such as mover_type=’fan’, fan_head_factor, fan_type, and material_type (‘*’ corresponds to the default options):

• fan_type:

  • ‘CentrifugalBackward’*

  • ‘CentrifugalStraight’

  • ‘VaneAxial’

  • ‘TubeAxial’

• fan_head_factor:

  • defaults to 1.45, see table 14

• material_type

  • ‘CarbonSteel’

  • ‘Fiberglass’

  • ‘StainlessSteel’*

  • ‘NickelAlloy’

Additionally, users may pass an argument ‘integer’ (defaults to True) whether the number of units should be restricted to an integer or not.

To select the correct fan type users must calculate the total head in inches of water (inH2O) and select the proper fan type from table 13. Additionally, the user must select the head factor (head_factor) from table 14.

Table 13. Typical Operating Ranges of Fans

Fan type	Flow rate (ACFM)	Total head inH2O
\(ACFM^a`\) inH2O
Centrifugal backward curved	1000-100000	1-40
Centrifugal straight radial	1000-20000	1-30
Vane axial	1000-800000	0.02-16
Tube axial	2000-800000	0.00-10

Finally, the purchase cost of the fan is given by base cost, material factor, and fan head factor, and is adjusted by user-defined currency units with the appropriate CE index value.. While, the base cost is given as a function of the ACFM (Q).

\[self.costing.purchase\_cost = head\_factor * material\_factor * self.costing.base\_cost\]

\[self.costing.base\_cost = self.costing.base\_cost\_per\_unit * self.costing.number\_of\_units\]

\[self.costing.base\_cost\_per\_unit = \exp{(\alpha_{1} - \alpha_{2}*\log{Q} + \alpha_{3}*(\log{Q})^{2})}\]

\[Q = self.Q / self.costing.number\_of\_units\]

Table 14. Head Factor, FH, for fans

Head (in H2O)	Centrifugal backward curved	Centrifugal straight radial	Vane axial	Tube Axial
5-8	1.15	1.15	1.15	1.15
9-15	1.30	1.30	1.30
16-30	1.45	1.45
31-40	1.55

Table 15. Materials of construction factor

Material Factor	FM
carbon_steel	1
fiberglass	1.8
stain_steel	2.5
nickel_alloy	5.0

Blower Cost

The blower cost is based on the brake horsepower, which can be calculated with the inlet volumetric flow rate and pressure (\(cfm\) and \(lbf/in^2\) respectively).

Additional arguments are required to estimate the blower cost such as mover_type=’blower’, blower_type, and materials of construction (‘*’ corresponds to the default options):

• blower_type:

  • ‘Centrifugal’*

  • ‘Rotary’

• material_type

  • ‘CarbonSteel’

  • ‘Aluminum’

  • ‘Fiberglass’

  • ‘StainlessSteel’*

  • ‘NickelAlloy’

Additionally, users may pass an argument ‘integer’ (defaults to True) whether the number of units should be restricted to an integer or not.

The material factors given in table 15 for the fans can be used. In addition, centrifugal blowers are available with cast aluminum blades with Mat_factor = 0.60.

The purchase cost is given by the material factor and base cost. While, the base cost is given by the power consumption in horsepower (Pc).

\[self.costing.purchase\_cost = material\_factor * self.costing.base\_cost\]

\[self.costing.base\_cost = self.costing.base\_cost\_per\_unit * self.costing.number\_of\_units\]

Centrigugal turbo blower (valid from PC = 5 to 1000 Hp):

\[self.costing.base\_cost\_per\_unit = \exp{(6.8929 + 0.7900*\log{Pc})}\]

Rotary straight-lobe blower (valid from PC = 1 to 1000 Hp):

\[self.costing.base\_cost\_per\_unit = \exp{(7.59176 + 0.79320*\log{Pc} - 0.012900*(\log{Pc})^{2})}\]

\[Pc = f(Q)\]

\[Q = self.Q / self.costing.number\_of\_units\]

Fired Heater

Indirect fired heaters, also called fired heaters, process heaters, and furnaces, are used to heat or vaporize process streams at elevated temperatures (beyond where steam is usually employed).

This method computes the purchase cost of the fired heater based on the heat duty, fuel used (fired_type), pressure design, and materials of construction (‘*’ corresponds to the default options):

• fuel_type:

  • ‘Fuel’*

  • ‘Reformer’

  • ‘Pyrolysis’

  • ‘HotWater’

  • ‘Salts’

  • ‘DowthermA’

  • ‘SteamBoiler’

• material_type

  • ‘CarbonSteel’*

  • ‘CrMoSteel’

  • ‘StainlessSteel’

Additionally, users may pass an argument ‘integer’ (defaults to True) whether the number of units should be restricted to an integer or not.

Table 16. Materials of construction factor

Material Factor	(FM)
carbon_steel	1
Cr-Mo_alloy	1.4
stain_steel	1.7

The pressure design factor is given by (where P is pressure in psig and it is valid between 500 to 3000 psig):

\[self.pressure\_factor == 0.986 - 0.0035*(P/500.00) + 0.0175*(P/500.00)^{2}\]

The base cost changes depending on the fuel type: fuel:

\[self.costing.base\_cost\_per\_unit = \exp{(0.32325 + 0.766*\log{heat\_duty})}\]

reformer:

\[self.costing.base\_cost\_per\_unit = 0.859*heat\_duty^{0.81}\]

pyrolysis:

\[self.costing.base\_cost\_per\_unit = 0.650*heat\_duty^{0.81}\]

hot_water:

\[self.costing.base\_cost\_per\_unit = \exp{(9.593- 0.3769*\log{heat\_duty} + 0.03434*(\log{heat\_duty})^{2})}\]

salts:

\[self.costing.base\_cost\_per\_unit = 12.32*heat\_duty^{0.64}\]

dowtherm_a:

\[self.costing.base\_cost\_per\_unit = 12.74*heat\_duty^{0.65}\]

steam_boiler:

\[self.costing.base\_cost\_per\_unit = 0.367*heat\_duty^{0.77}\]

\[self.costing.base\_cost = self.costing.base\_cost\_per\_unit * self.costing.number\_of\_units\]

Finally, the purchase cost (adjusted by user-defined currency units with the appropriate CE index value)is given by:

\[self.purchase\_cost = pressure\_design * material\_factor * base\_cost\]

Cost of Pressure Vessels and Towers for Distillation

Pressure vessels cost is based on the weight of the vessel, the cost of platforms and ladders can be included, and the cost of internal packing or trays can be calculated as well.

This method constructs by default the cost of pressure vessels with platforms and ladders, and trays cost can be calculated if trays = True. This method requires a few arguments to build the cost of vessel. We recommend using this method to cost reactors (StoichiometricReactor, CSTR` or PFR`), flash tanks, vessels, and distillation columns (‘*’ corresponds to the default options):

• vertical:

  • False*

  • True

• material_type

  • ‘CarbonSteel’*

  • ‘LowAlloySteel’

  • ‘StainlessSteel304’

  • ‘StainlessSteel316’

  • ‘Carpenter20CB3’

  • ‘Nickel200’

  • ‘Money400’

  • ‘Inconel600’

  • ‘Incoloy825’

  • ‘Titanium’

• shell_thickness

  • material property (including pressure allowance), defaults to 1.25 inches (Pyomo units)

• weight_limit:

  • 1: 1000 to 920,000 lb*

  • 2: 9000 to 2.5M lb (only for vertical vessels)

• aspect_ratio_range (all in ft D: diameter, L: length):

  • 1: 3 < D < 21, 12 < L < 40*

  • 2: 3 < D < 24, 27 < L < 170; only for vertical vessels

• include_platform_ladders:

  • True*

  • False

• vessel_diameter:

  • component to use as diameter variable, defaults to unit.diameter

• vessel_length:

  • component to use as length variable, defaults to unit.length

• number_of_units:

  • integer or Pyomo component to use for number of parallel units to be costed, defaults to 1

• number_of_trays:

  • component to use for number of distillation trays in vessel, defaults to None

• tray_material:

  • ‘CarbonSteel’*

  • ‘StainlessSteel303’

  • ‘StainlessSteel316’

  • ‘Carpenter20CB3’

  • ‘Monel’

• tray_type:

  • ‘Sieve’*

  • ‘Valve’

  • ‘BubbleCap’

By adding reference parameter, the method can be constructed in any pyomo costing block. Since the generic models do not include the variables required to cost these type of units, the user must create the blocks and variables.

For example:

m.fs.unit = Block()
m.fs.unit.diameter = Var()
m.fs.unit.length = Var().
m.fs.unit.costing = pyo.Block()
vessel_costing_method = SSLWCostingData.costing_vessel(m.fs.unit.costing, args).

Table 17. Materials of construction factor and material density

Material Factor	(FM)	metal density (\(lb/in^3\))
carbon_steel	1	0.284
low_alloy_steel	1.2	0.271
stain_steel_304	1.7	0.270
stain_steel_316	2.1	0.276
carpenter_20CB-3	3.2	0.292
nickel_200	5.4	0.3216
monel_400	3.6	0.319
inconel_600	3.9	0.3071
incoloy_825	3.7	0.2903
titanium	7.7	0.1628

Vessel Cost

The weight of the unit is calculated based on the metal density, length, diameter, and shell thickness. shell_thickness is a parameter initialized to 1.25, however, the user must calculate the shell wall minimum thickness computed from the ASME pressure vessel code (tp) add the average vessel thickness, the necessary wall thickness (tE), and select the appropriate shell_thickness.

\[\begin{split}self.weight == \pi * ((D*12) + self.shell\_thickness) * ((L*12) \\ +(0.8*D*12))*self.shell\_thickness*self.material\_density\end{split}\]

The base cost of the vessel is given by: Horizontal vessels (1: 1000 < W < 920,000 lb):

\[self.costing.base\_cost\_per\_unit = \exp{(8.9552 - 0.2330*\log{weight} + 0.04333*(\log{weight})^{2})}\]

Vertical vessels (1: 4200 < W < 1M lb):

\[self.costing.base\_cost\_per\_unit = \exp{(8.9552 - 0.2330*\log{weight} + 0.04333*(\log{weight})^{2})}\]

Vertical vessels (2: 9,000 < W < 2.5M lb):

\[self.costing.base\_cost\_per\_unit = \exp{(7.2756 - 0.18255*\log{weight} + 0.02297*(\log{weight})^{2})}\]

\[self.costing.base\_cost = self.costing.base\_cost\_per\_unit * self.costing.number\_of\_units\]

\[weight = self.weight / self.costing.number\_of\_units\]

The vessel purchase cost (adjusted by user-defined currency units with the appropriate CE index value) is given by:

\[\begin{split}self.vessel\_purchase\_cost = material\_factor * self.base\_cost \\ + (self.base\_cost\_platforms\_ladders * self.costing.number\_of\_units)\end{split}\]

note that if PL = False, the cost of platforms and ladders is not included.

The final purchase cost is given by:

\[self.purchase\_cost = self.vessel\_purchase\_cost + (self.purchase\_cost\_trays * self.costing.number\_of\_units)\]

note that if plates = False, the cost of trays is not included.

Base Cost of Platforms and ladders

The cost of platforms and ladders is based on the diameter and length in ft. Horizontal vessels (1: 3 < D < 12 ft):

\[self.base\_cost\_platforms\_ladders = 20059*D^{0.20294}\]

Vertical vessels (1: 3 < D < 12 ft and 12 < L < 40 ft):

\[self.base\_cost\_platforms\_ladders = 361.8*D^{0.73960} * L^{0.70684}\]

Vertical vessels (2: 3 < D < 24 ft and 27 < L < 170 ft):

\[self.base\_cost\_platforms\_ladders = 300.9*D^{0.63316} * L^{0.80161}\]

Purchase Cost of Plates

The cost of plates is based on the number or trays, the type of trays used, and materials of construction. Tray type factor (tray_factor) is 1.0 for sieve trays, 1.18 for valve trays (valve), and 1.87 for bubble cap trays (bubble_cap). The number of trays factor (number_tray_factor) is equal to 1 if the number of trays is greater than 20. However, if the number of trays is less than 20, the number_tray_factor is given by:

\[self.number\_tray\_factor = \frac{2.25}{1.0414^{NT}}\]

The materials of construction factor is calculated using the following equation:

\[\alpha_1 + \alpha_2 * D\]

where alphas for different materials of construction are given in table 18.

Table 18. Materials of construction factor

Material	alpha1	alpha2
carbon_steel	1	0
stain_steel_303	1.189	0.0577
stain_steel_316	1.401	0.0724
carpenter_20CB-3	1.525	0.0788
monel_400	2.306	0.1120

The tray base cost is then calculated as:

\[self.base\_cost\_trays = 468.00*\exp{(0.1739*D)}\]

The purchase cost of the trays (adjusted by user-defined currency units with the appropriate CE index value) is given by:

\[\begin{split}self.purchase\_cost\_trays = self.number\_trays * self.number\_tray\_factor \\ * self.type\_tray\_factor * self.tray\_material\_factor * self.base\_cost\_trays\end{split}\]

Module Classes

class idaes.models.costing.SSLW.SSLWCosting(*args, **kwds)

Parameters:

• rule (function) – A rule function or None. Default rule calls build().

• concrete (bool) – If True, make this a toplevel model. Default - False.

• ctype (class) –

  Pyomo ctype of the block. Default - pyomo.environ.Block

  Config args

• initialize (dict) – ProcessBlockData config for individual elements. Keys are BlockData indexes and values are dictionaries with config arguments as keys.

• idx_map (function) – Function to take the index of a BlockData element and return the index in the initialize dict from which to read arguments. This can be provided to override the default behavior of matching the BlockData index exactly to the index in initialize.

Returns:

(SSLWCosting) New instance

class idaes.models.costing.SSLW.SSLWCostingData(component)

build_global_params()

This is where we can declare any global parameters we need, such as Lang factors, or coefficients for costing methods that should be shared across the process.

You can do what you want here, so you could have e.g. sub-Blocks for each costing method to separate the parameters for each method.

build_process_costs()

This is where you do all your process wide costing. This is completely up to you, but you will have access to the following aggregate costs:

1. self.aggregate_capital_cost

2. self.aggregate_fixed_operating_cost

3. self.aggregate_variable_operating_cost

4. self.aggregate_flow_costs (indexed by flow type)

cost_blower(blower_type=BlowerType.Centrifugal, material_type=BlowerMaterial.StainlessSteel, integer=True)

Generic costing method for blowers.

Parameters:

• blower_type – BlowerType Enum indicating type of type of equipment, default = BlowerType.Centrifugal.

• material_type – BlowerMaterial Enum indicating material of construction, default = BlowerMaterial.StainlessSteel.

• integer – whether the number of units should be constrained to be an integer or not (default = True).

cost_compressor(compressor_type=CompressorType.Centrifugal, drive_type=CompressorDriveType.ElectricMotor, material_type=CompressorMaterial.StainlessSteel, integer=True)

Generic costing method for compressors.

Parameters:

• compressor_type – CompressorType Enum indicating type of type of equipment, default = CompressorType.Centrifugal.

• material_type – CompressorMaterial Enum indicating material of construction, default = CompressorMaterial.StainlessSteel.

• drive_type – CompressorDriveType Enum indicating type of type of drive to be used, default = CompressorDriveType.ElectricMotor.

• integer – whether the number of units should be constrained to be an integer or not (default = True).

cost_fan(fan_type=FanType.CentrifugalBackward, fan_head_factor=1.45, material_type=FanMaterial.StainlessSteel, integer=True)

Generic costing method for fans.

Parameters:

• fan_type – FanType Enum indicating type of type of equipment, default = FanType.CentrifugalBackward.

• fan_head_factor – (float) fan head factor (default=1.45).

• material_type – FanMaterial Enum indicating material of construction, default = FanMaterial.StainlessSteel.

• integer – whether the number of units should be constrained to be an integer or not (default = True).

cost_fired_heater(heat_source=HeaterSource.Fuel, material_type=HeaterMaterial.CarbonSteel, integer=True)

Generic costing method for fired heaters.

Parameters:

• heat_source – HeaterSource Enum indicating type of source of heat, default = HeaterSource.Fuel.

• material_type – HeaterMaterial Enum indicating material of construction, default = HeaterMaterial.CarbonSteel.

• integer – whether the number of units should be constrained to be an integer or not (default = True).

cost_heat_exchanger(hx_type=HXType.Utube, material_type=HXMaterial.StainlessSteelStainlessSteel, tube_length=HXTubeLength.TwelveFoot, integer=True)

Heat exchanger costing method.

This method computes the purchase cost (CP) for a shell and tube heat exchanger (Eq. 22.43), the model computes the base cost (CB for 4 types of heat exchangers, such as floating head, fixed head, U-tube, and Kettle vaporizer), construction material factor (mat_factor), pressure design factor (pressure_factor), and tube length correction factor (length_factor), using Chemical Engineering base cost index of 500.

Purchase Cost = pressure_factor *

material_factor * length_factor * base_cost_per_unit * number_of_units

Parameters:

• hx_type – HXType Enum indicating type of heat exchanger design, default = HXType.Utube.

• material_type – HXMaterial Enum indicating material of construction, default = HXMaterial.StainlessSteelStainlessSteel.

• tube_length – HXTubeLength Enum indicating length of HX tubes, default = HXTubeLength.TwelveFoot.

• integer – whether the number of units should be constrained to be an integer or not (default = True).

cost_horizontal_vessel(material_type=VesselMaterial.CarbonSteel, shell_thickness=<pyomo.core.expr.numeric_expr.NPV_ProductExpression object>, include_platforms_ladders=True, vessel_diameter=None, vessel_length=None, number_of_units=1)

Specific case of vessel costing method for horizontal vessels.

Arguments which do not apply to horizontal vessels are excluded.

Parameters:

• material_type – VesselMaterial Enum indicating material of construction, default = VesselMaterial.CarbonSteel.

• shell_thickness – thickness of vessel shell, including pressure allowance. Default = 1.25 inches.

• include_platforms_ladders – whether to include platforms and ladders in costing, default = True.

• vessel_diameter – Pyomo component representing vessel diameter. If not provided, assumed to be named “diameter”

• vessel_length – Pyomo component representing vessel length. If not provided, assumed to be named “length”.

• number_of_units – Integer or Pyomo component representing the number of parallel units to be costed, default = 1.

cost_pressure_changer(mover_type='compressor', **kwargs)

Gateway method for costing pressure changers. This method attempts to determine the type of pressure changer from the compressor and thermodynamic assumption config arguments and then calls th appropriate sub-method. As such, keyword arguments to this method will depend on the sub-method called. Users are generally encouraged to call the specific sub-methods directly as required.

Parameters:

mover_type – optional argument to indicate type of pressure changer.

cost_pump(pump_type=PumpType.Centrifugal, material_type=PumpMaterial.StainlessSteel, pump_type_factor=1.4, motor_type=PumpMotorType.Open, integer=True)

Generic costing method for pumps.

Parameters:

• pump_type – PumpType Enum indicating type of type of equipment, default = PumpType.Centrifugal.

• material_type – PumpMaterial Enum indicating material of construction, default = PumpMaterial.StainlessSteel. Material type is tied to PumpType.

• pump_type_factor – empirical factor for centrigual pumps based on table in source. Valid values are [1.1, 1.2, 1.3, 1.4 (default), 2.1, 2.2].

• motor_type – PumpMotorType Enum indicating type of type of motor to be used, default = PumpMotorType.Open.

• integer – whether the number of units should be constrained to be an integer or not (default = True).

cost_turbine(integer=True)

Generic costing method for turbines.

Parameters:

integer – whether the number of units should be constrained to be an integer or not (default = True).

cost_vertical_vessel(material_type=VesselMaterial.CarbonSteel, shell_thickness=<pyomo.core.expr.numeric_expr.NPV_ProductExpression object>, weight_limit=1, aspect_ratio_range=1, include_platforms_ladders=True, vessel_diameter=None, vessel_length=None, number_of_units=1, number_of_trays=None, tray_material=TrayMaterial.CarbonSteel, tray_type=TrayType.Sieve)

Specific case of vessel costing method for vertical vessels.

Parameters:

• material_type – VesselMaterial Enum indicating material of construction, default = VesselMaterial.CarbonSteel.

• shell_thickness – thickness of vessel shell, including pressure allowance. Default = 1.25 inches.

• weight_limit – 1: (default) 1000 to 920,000 lb, 2: 4200 to 1M lb.

• aspect_ratio_range – default = 1; 1: 3 < D < 21 ft, 12 < L < 40 ft, 2: 3 < D < 24 ft; 27 < L < 170 ft.

• include_platforms_ladders – whether to include platforms and ladders in costing , default = True.

• vessel_diameter – Pyomo component representing vessel diameter. If not provided, assumed to be named “diameter”

• vessel_length – Pyomo component representing vessel length. If not provided, assumed to be named “length”.

• number_of_units – Integer or Pyomo component representing the number of parallel units to be costed, default = 1.

• number_of_trays – Pyomo component representing the number of distillation trays in vessel (default=None)

• tray_material – Only required if number_of_trays is not None. TrayMaterial Enum indicating material of construction for distillation trays, default = TrayMaterial.CarbonSteel.

• tray_type – Only required if number_of_trays is not None. TrayType Enum indicating type of distillation trays to use, default = TrayMaterial.Sieve.

cost_vessel(vertical=False, material_type=VesselMaterial.CarbonSteel, shell_thickness=<pyomo.core.expr.numeric_expr.NPV_ProductExpression object>, weight_limit=1, aspect_ratio_range=1, include_platforms_ladders=True, vessel_diameter=None, vessel_length=None, number_of_units=1, number_of_trays=None, tray_material=TrayMaterial.CarbonSteel, tray_type=TrayType.Sieve)

Generic vessel costing method.

Parameters:

• vertical – alignment of vessel; vertical if True, horizontal if False (default=False).

• material_type – VesselMaterial Enum indicating material of construction, default = VesselMaterial.CarbonSteel.

• shell_thickness – thickness of vessel shell, including pressure allowance. Default = 1.25 inches.

• weight_limit – 1: (default) 1000 to 920,000 lb, 2: 4200 to 1M lb. Option 2 is only valid for vertical vessels.

• aspect_ratio_range – vertical vessels only, default = 1; 1: 3 < D < 21 ft, 12 < L < 40 ft, 2: 3 < D < 24 ft; 27 < L < 170 ft.

• include_platforms_ladders – whether to include platforms and ladders in costing , default = True.

• vessel_diameter – Pyomo component representing vessel diameter. If not provided, assumed to be named “diameter”

• vessel_length – Pyomo component representing vessel length. If not provided, assumed to be named “length”.

• number_of_units – Integer or Pyomo component representing the number of parallel units to be costed, default = 1.

• number_of_trays – Pyomo component representing the number of distillation trays in vessel (default=None)

• tray_material – Only required if number_of_trays is not None. TrayMaterial Enum indicating material of construction for distillation trays, default = TrayMaterial.CarbonSteel.

• tray_type – Only required if number_of_trays is not None. TrayType Enum indicating type of distillation trays to use, default = TrayMaterial.Sieve.

static initialize_build(*args, **kwargs)

Here we can add initialization steps for the things we built in build_process_costs.

Note that the aggregate costs will be initialized by the framework.