Unit Model Costing¶
The IDAES Process Modeling Framework includes support for incorporating costing of unit operations into a flowsheet to allow for calculation and optimization of process costs. Cost Correlations are implemented using unit costing sub-modules to allow users to easily develop and incorporate their own costing models.
Contents
Introduction¶
All unit models within the core IDAES model library include a get_costing method which can be called to include cost correlations for an instance of that unit. The get_costing method for each unit takes a number of arguments used to specify the basis for costing each piece of equipment. Details are given for each unit model later in this documentation, however, all get_costing methods take the following two arguments:
module - this argument specifies the costing module to use when constructing the constraints and associated variables. if not provided, this defaults to the standard IDAES costing module.
year - this argument sets the year to which all costs should be normalized (CE index 2010 to 2019)
When get_costing is called on an instance of a unit model, a new sub-block is created on that unit named costing (i.e. flowsheet.unit.costing). All variables and constraints related to costing will be constructed within this new block (see detailed documentation for each unit for details on these variables and constraints).
In addition, the first time get_costing is called for a unit operation within a flowsheet, an additional costing block is created on the flowsheet object (i.e. flowsheet.unit.costing) in order to hold any global parameters relating to costing. The most common of these paramters is the cost normalization parameter based on the year selected by the user.
The unit costing module also contains an initialize method which can be used to estimate initial values for costing variables based on the current state of the associated unit model. This method can be called directly from the unit_costing module to initialize a specific costing block, or can be incorporated into a unit model initialization procedure. This method has been incorporated into the initialize method of all the models in the core unit model library. Therefore, if get_costing() is called before unit.initialize(), the initialize method will deactivate the costing block, initialize the unit model as normal, and then activate the costing block and initialize costing block.
Note
The global paramters are created when the first instance of get_costing is called and use the values provided there for initialization. Subsequent get_costing calls use the existing paramters, and do not change the initialized values. i.e. any “year” argument provided to a get_costing call after the first will be ignored.
Table 1. Main Variables added to the unit block (“self.costing”).
Variable |
Symbol |
Units |
Notes |
|---|---|---|---|
Purchase cost |
\(purchase\_cost\) |
dollars |
Purchase cost |
Base cost per unit |
\(base\_cost_per_unit\) |
unitless |
Base cost per unit |
Base cost |
\(base\_cost\) |
unitless |
Base cost (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 latest, the user must provide an mip solver. Use the global costing argument for this purpose (integer_n_units=True or False).
Example¶
Below is a simple example of how to add cost correlations to a flowsheet including a heat exchanger using the default IDAES costing module.
from pyomo.environ import (ConcreteModel, SolverFactory)
from pyomo.util.calc_var_value import calculate_variable_from_constraint
from idaes.core import FlowsheetBlock
from idaes.generic_models.unit_models.heat_exchanger import \
(HeatExchanger, HeatExchangerFlowPattern)
from idaes.generic_models.properties import iapws95
from idaes.core.util.model_statistics import degrees_of_freedom
m = ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.properties = iapws95.Iapws95ParameterBlock()
m.fs.unit = HeatExchanger(default={
"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.unit.get_costing(module=costing, length_factor='12ft')
m.fs.unit.initialize()
opt = SolverFactory('ipopt')
opt.options = {'tol': 1e-6, 'max_iter': 50}
results = opt.solve(m, tee=True)
Units¶
It is important to highlight that the costing method interrogates the property package to determine the units of this model, if the user provided the correct units in the metadata dictionary (see property models for additional information), the model units will be converted to the right units. For example: in this example area is in m^2, while the cost correlations for heat exchangers require units to be in ft^2. Therefore, the costing method will convert the units to ft^2. The use of Pyomo-unit conversion tools is under development.
IDAES Costing Module¶
A default 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 appropiate).
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
Users should refer to the reference above for details of the costing correlations, however, a summary of this methods is provided below.
Table 2. Cost basis for each unit model.
Unit Model |
Basis |
Units |
|---|---|---|
heat exchanger |
\(area\) |
ft^2 |
pump |
\(fluid_{work}\) |
ft^3/s |
compressor |
\(mechanical_{work}\) |
hp |
turbine |
\(mechanical_{work}\) |
hp |
vessels |
\(D and L\) |
ft |
fired heaters |
\(heat\_duty\) |
BTU/hr |
Heat Exchanger Cost¶
The purchse cost is computed based on the base unit cost and three correction factors (Eq. 22.43 in Seider et al.). The base cost is computed depending on the heat exchanger type selected by the user:
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
CE_index - is a global parameter for Chemical Enginering cost index for years 2010-2019
hx_os - heat exchanger oversize factor (default = 1)
area is a reference object and (self.area is the model variable)
The heat exchanger costing method has three arguments, hx_type = heat exchanger type, FM_Mat = construction material factor, and FL = tube length factor.
hx_type : ‘floating_head’, ‘fixed_head’, ‘U-tube’*, ‘Kettle_vap’
material factor (Mat_factor): ‘stain_steel’*, ‘carb_steel’
tube length (length_factor): ‘8ft’, ‘12ft’*, ‘16ft’, ‘20ft’
where ‘*’ corresponds to the default options, FL and FM_MAT are pyomo-mutable parameters fixed based on user selection.
Table 3. Base cost factors for heat exchanger type.
Tube Length (ft) |
\(\alpha_{1}\) |
\(\alpha_{2}\) |
\(\alpha_{3}\) |
|---|---|---|---|
floating_head |
11.9052 |
0.8709 |
0.09005 |
fixed_head |
11.2927 |
0.8228 |
0.09861 |
U-tube |
11.3852 |
0.9186 |
0.09790 |
Kettle_vap |
12.2052 |
0.8709 |
0.09005 |
Table 4. Tube-Length correction factor.
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.)
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 |
Note that Mat_factor argument should be provided a string, for example: Mat_factor:’carbon steel/carbon steel’.
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 simply pressure changer (fan, blower, etc.). The get_costing method currently supports costing of pumps, turbines, and compressors. The method authomatically interrogates the flowsheet object to determine if the unit is being used as a pump, turbine, or compressor.
The get_costing 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 |
Additionally, some unit types have different sub-types which can be costed appropiately. In these cases, an additional argument is provided to get_costing 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).
DOE/NETL, 2015, report. Cost and performance Baseline for Fossil Energy Plants. Volume 1a: Bituminous Coal (PC) and Natural Gas to Electricity. Revision 3
Pump Cost Model¶
Three subtypes are supported for costing of pumps, which can be set using the “pump_type” argument.
Centrifugal pumps (pump_type=’centrifugal’)
External gear pumps (pump_type=’external’)
Reciprocating Plunger pumps (pump_type=’reciprocating’)
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:
pump_type_factor = ‘1.4’ (see Table 6)
pump_motor_type_factor = ‘open’, ‘enclosed’, ‘explosion_proof’
Based on user’s inputs the get_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.
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.)
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:
A centrifugal pump is usually driven by an electric motor, the self.costing.motor_purchase_cost is calculated based on the power consumption.
Efficiencies are valid for PB in the range of 1 to 1500Hp 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.
. math:: self.costing.self.costing.pump_base_cost_perunit = exp{(7.6964 + 0.1986log{Q} + 0.0291(log{Q})^{2})}
Reciprocating Plunger Pumps¶
The cost correlation method used here is based on the brake horsepower (PB).
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.
mover_type= ‘compressor’ or ‘fan’ or ‘blower’ (uper/lower case sensitive)
Compressor Cost¶
The compressor cost is based on the mechanical work of the unit. Additional arguments are required to estimate the cost such as compressor type, driver mover type, and material factor (Mat_factor).
compressor_type = ‘centrifugal’, ‘reciprocating’, ‘screw’
driver_mover_type = ‘electrical_motor’, ‘steam_turbine’, ‘gas_turbine’
Mat_factor = ‘carbon_steel’, ‘stain_steel’, ‘nickel_alloy’
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 factor (Mat_factor).
fan_type = ‘centrifugal_backward’, ‘centrifugal_straight’, ‘vane_axial’, ‘tube_axial’
fan_head_factor = see table 14
Mat_factor = ‘carbon_steel’, ‘fiberglass’, ‘stain_steel’, ‘nickel_alloy’
To select the correct fan type users must calculate the total head in 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. While, the base cost is given as a function of the ACFM (Q).
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, respectivelly). Additional arguments are required to estimate the blower cost such as mover_type=’blower’, blower_type, and material of construction factor (Mat_factor).
blower_type = ‘centrifugal’, ‘rotary’
Mat_factor = ‘carbon_steel’, ‘aluminum’, ‘fiberglass’, ‘stain_steel’, ‘nickel_alloy’
where 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).
Centrigugal turbo blower (valid from PC = 5 to 1000 Hp):
Rotary straight-lobe blower (valid from PC = 1 to 1000 Hp):
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 (Mat_factor).
fuel_type = ‘fuel’, ‘reformer’, ‘pyrolysis’, ‘hot_water’, ‘salts’, ‘dowtherm_a’, ‘steam_boiler’
Mat_factor = see table 16
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):
The base cost changes depending on the fuel type: fuel:
reformer:
pyrolysis:
hot_water:
salts:
dowtherm_a:
steam_boiler:
Finally, the purchase cost is given by:
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 defaul 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 (CSTR or PFR), flash tanks, vessels, and distillation columns.
alignment = ‘horizontal’, ‘vertical’
Mat_factor = ‘carbon_steel’
weight_limit = ‘option1’, ‘option2’ (option 1: 1000 to 920,000 lb, option 2: 9000 to 2.5M lb only for vertical vessels)
L_D_range = ‘option1’, ‘option2’ (option 1: 3 < D < 21, 12 < L < 40; option 2: 3 < D < 24, 27 < L < 170; all in ft D: diameter, L: length) only for vertical vessels
PL=’True’, ‘False’: to build platforms and ladders cost
plates = ‘True’, ‘False’: to build tray cost for distillation columns
tray_mat_factor = ‘carbon_steel’ see table 18
tray_type = ‘sieve’
number_tray = 10
ref_parameter_diameter=None
ref_parameter_length=None
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(). Then m.fs.unit.costing = pyo.Block() and call vessel_costing method = vessel_costing(m.fs.unit.costing, args).
Table 17. Materials of construction factor and material density
Material Factor |
(FM) |
methal 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 methal density, length, Diameter, and shell thickness. shel_thickness is a parameter initialized to 1.25, however, the user must calculate the shell wall minimum thickness computd from the ASME pressure vessel code (tp) add the average vessel thickness, the necessary wall thickness (tE), and select the appropriate shell_thickness.
The base cost of the vessel is given by: Horizontal vessels (option1: 1000 < W < 920,000 lb):
Vertical vessels (option1: 4200 < W < 1M lb):
Vertical vessels (option2: 9,000 < W < 2.5M lb):
The vessel purchase cost is given by:
note that if PL = ‘False’, the cost of platforms and ladders is not included.
The final purchase cost is given by:
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 diamter and length in ft. Horizontal vessels (option1: 3 < D < 12 ft):
Vertical vessels (option1: 3 < D < 12 ft and 12 < L < 40 ft):
Vertical vessels (option2: 3 < D < 24 ft and 27 < L < 170 ft):
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:
The materials of construction factor is calculated using the following equation:
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:
The purchase cost of the trays is given by: