Process Costing Using SSLW Process and Product Design Principles ================================================================ .. contents:: Contents :depth: 4 Introduction ------------ .. rubric:: 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 :ref:`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 :math:`purchase\_cost` dollars Equipment cost adjusted for pressure, material, length and quantity factors Base cost per unit :math:`base\_cost\_per\_unit` unitless Base cost per unit before adjustment (from costing correlations) Base cost :math:`base\_cost` unitless Base cost of total set of units (base cost per unit * number of units) Number of units :math:`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 :math:`area` :math:`ft^2` pump :math:`fluid_{work}` :math:`ft^3/s` compressor :math:`mechanical_{work}` :math:`hp` turbine :math:`mechanical_{work}` :math:`hp` vessels :math:`D , L` :math:`ft` fired heaters :math:`heat\_duty` :math:`BTU/hr` =========================== ========================= ============== Example ^^^^^^^ Below is a example of how to add and solve an SSLW costing block for a flowsheet including a heat exchanger: .. code:: python 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 purchse 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. .. math:: self.costing.purchase\_cost = pressure\_factor*material\_factor*L\_factor*self.costing.base\_cost .. math:: self.costing.base\_cost\_per\_unit = \exp{(\alpha_{1} - \alpha_{2}*\log{area*hx\_os} + \alpha_{3}*(\log{area*hx\_os})^{2})} .. math:: self.costing.base\_cost = self.costing.base\_cost\_per\_unit * self.costing.number\_of\_units .. math:: 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 :math:`\alpha_{1}` :math:`\alpha_{2}` :math:`\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.) .. math:: 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). .. math:: 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. .. math:: 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. .. math:: S = QH^{0.5} .. math:: self.costing.pump\_base\_cost\_per\_unit = \exp{(9.7171 - 0.6019*\log{S} + 0.0519*(\log{S})^{2})} .. math:: self.costing.pump\_purchase\_cost = F_{T}*material\_factor*self.costing.pump\_base\_cost .. math:: self.costing.base\_cost = self.costing.pump\_base\_cost\_per\_unit * self.costing.number\_of\_units .. math:: 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 :math:`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. .. math:: self.costing.motor\_purchase\_cost = FT * self.costing.motor\_base\_cost (Eq. 22.20) .. math:: self.costing.motor\_base\_cost = self.costing.motor\_base\_cost\_per\_unit * self.costing.number\_of\_units .. math:: Q = self.Q / self.costing.number\_of\_units .. math:: 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) .. math:: 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) .. math:: \eta_{P} = -0.316 + 0.24015*\log{Q} - 0.01199(\log{Q})^{2} (Eq. 22.17) .. math:: \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 * :math:`\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. .. math:: self.costing.pump\_purchase\_cost = material\_factor * self.costing.pump\_base\_cost .. math:: self.costing.pump\_base\_cost = self.costing.pump\_base\_cost\_per\_unit * self.costing.number\_of\_units .. math:: self.costing.self.costing.pump\_base\_cost\_per\_unit = \exp{(7.6964 + 0.1986\log{Q} + 0.0291(\log{Q})^{2})} .. math:: 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. .. math:: self.costing.pump\_purchase\_cost = material\_factor * self.costing.pump\_base\_cost (Eq. 22.22) .. math:: self.costing.pump\_base\_cost = self.costing.pump\_base\_cost\_per\_unit * self.costing.number\_of\_units .. math:: self.costing.pump\_base\_cost\_per\_unit = \exp{(7.8103 + 0.26986\log{PB} + 0.06718(\log{PB})^{2})} (Eq. 22.23) .. math:: PB = f(Q) .. math:: 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. .. math:: self.costing.purchase\_cost = F_{D} * material\_factor * self.costing.base\_cost .. math:: self.costing.base\_cost = self.costing.base\_cost\_per\_unit * self.costing.number\_of\_units .. math:: self.costing.base\_cost\_per\_unit = \exp{(\alpha_{1} + \alpha_{2}*\log{mechanical_{work}})} .. math:: 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 :math:`\alpha_{1}` :math:`\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 :math:`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). .. math:: self.costing.purchase\_cost = head\_factor * material\_factor * self.costing.base\_cost .. math:: self.costing.base\_cost = self.costing.base\_cost\_per\_unit * self.costing.number\_of\_units .. math:: self.costing.base\_cost\_per\_unit = \exp{(\alpha_{1} - \alpha_{2}*\log{Q} + \alpha_{3}*(\log{Q})^{2})} .. math:: 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 (:math:`cfm` and :math:`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). .. math:: self.costing.purchase\_cost = material\_factor * self.costing.base\_cost .. math:: 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): .. math:: self.costing.base\_cost\_per\_unit = \exp{(6.8929 + 0.7900*\log{Pc})} Rotary straight-lobe blower (valid from PC = 1 to 1000 Hp): .. math:: self.costing.base\_cost\_per\_unit = \exp{(7.59176 + 0.79320*\log{Pc} - 0.012900*(\log{Pc})^{2})} .. math:: Pc = f(Q) .. math:: 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): .. math:: 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: .. math:: self.costing.base\_cost\_per\_unit = \exp{(0.32325 + 0.766*\log{heat\_duty})} reformer: .. math:: self.costing.base\_cost\_per\_unit = 0.859*heat\_duty^{0.81} pyrolysis: .. math:: self.costing.base\_cost\_per\_unit = 0.650*heat\_duty^{0.81} hot_water: .. math:: self.costing.base\_cost\_per\_unit = \exp{(9.593- 0.3769*\log{heat\_duty} + 0.03434*(\log{heat\_duty})^{2})} salts: .. math:: self.costing.base\_cost\_per\_unit = 12.32*heat\_duty^{0.64} dowtherm_a: .. math:: self.costing.base\_cost\_per\_unit = 12.74*heat\_duty^{0.65} steam_boiler: .. math:: self.costing.base\_cost\_per\_unit = 0.367*heat\_duty^{0.77} .. math:: 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: .. math:: 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: .. code:: python 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 (:math:`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. .. math:: self.weight == \pi * ((D*12) + self.shell\_thickness) * ((L*12) \\ +(0.8*D*12))*self.shell\_thickness*self.material\_density The base cost of the vessel is given by: Horizontal vessels (1: 1000 < W < 920,000 lb): .. math:: 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): .. math:: 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): .. math:: self.costing.base\_cost\_per\_unit = \exp{(7.2756 - 0.18255*\log{weight} + 0.02297*(\log{weight})^{2})} .. math:: self.costing.base\_cost = self.costing.base\_cost\_per\_unit * self.costing.number\_of\_units .. math:: 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: .. math:: self.vessel\_purchase\_cost = material\_factor * self.base\_cost \\ + (self.base\_cost\_platforms\_ladders * self.costing.number\_of\_units) note that if PL = `False`, the cost of platforms and ladders is not included. The final purchase cost is given by: .. math:: 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): .. math:: self.base\_cost\_platforms\_ladders = 20059*D^{0.20294} Vertical vessels (1: 3 < D < 12 ft and 12 < L < 40 ft): .. math:: 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): .. math:: 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: .. math:: self.number\_tray\_factor = \frac{2.25}{1.0414^{NT}} The materials of construction factor is calculated using the following equation: .. math:: \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: .. math:: 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: .. math:: self.purchase\_cost\_trays = self.number\_trays * self.number\_tray\_factor \\ * self.type\_tray\_factor * self.tray\_material\_factor * self.base\_cost\_trays Module Classes ^^^^^^^^^^^^^^ .. module:: idaes.models.costing.SSLW .. autoclass:: SSLWCosting :members: .. autoclass:: SSLWCostingData :members: