#################################################################################
# WaterTAP Copyright (c) 2020-2024, The Regents of the University of California,
# through Lawrence Berkeley National Laboratory, Oak Ridge National Laboratory,
# National Renewable Energy Laboratory, and National Energy Technology
# Laboratory (subject to receipt of any required approvals from the U.S. Dept.
# of Energy). All rights reserved.
#
# Please see the files COPYRIGHT.md and LICENSE.md for full copyright and license
# information, respectively. These files are also available online at the URL
# "https://github.com/watertap-org/watertap/"
#################################################################################
import pyomo.environ as pyo
from watertap.costing.util import (
register_costing_parameter_block,
make_capital_cost_var,
)
def build_surrogate_crystallizer_cost_param_block(blk):
blk.steam_pressure = pyo.Var(
initialize=3,
units=pyo.units.bar,
doc="Steam pressure (gauge) for crystallizer heating: 3 bar default based on Dutta example",
)
blk.efficiency_pump = pyo.Var(
initialize=0.7,
units=pyo.units.dimensionless,
doc="Crystallizer pump efficiency - assumed",
)
blk.pump_head_height = pyo.Var(
initialize=1,
units=pyo.units.m,
doc="Crystallizer pump head height - assumed, unvalidated",
)
# Crystallizer operating cost information from literature
blk.fob_unit_cost = pyo.Var(
initialize=675000,
doc="Forced circulation crystallizer reference free-on-board cost (Woods, 2007)",
units=pyo.units.USD_2007,
)
blk.ref_capacity = pyo.Var(
initialize=1,
doc="Forced circulation crystallizer reference crystal capacity (Woods, 2007)",
units=pyo.units.kg / pyo.units.s,
)
blk.ref_exponent = pyo.Var(
initialize=0.53,
doc="Forced circulation crystallizer cost exponent factor (Woods, 2007)",
units=pyo.units.dimensionless,
)
blk.iec_percent = pyo.Var(
initialize=1.43,
doc="Forced circulation crystallizer installed equipment cost (Diab and Gerogiorgis, 2017)",
units=pyo.units.dimensionless,
)
blk.steam_cost = pyo.Var(
initialize=0.004,
units=pyo.units.USD_2018 / (pyo.units.meter**3),
doc="Steam cost, Panagopoulos (2019)",
)
costing = blk.parent_block()
costing.register_flow_type("steam", blk.steam_cost)
[docs]def cost_surrogate_crystallizer(blk):
"""
Function for costing the surrogate crystallizer by the mass flow of produced crystals.
The operating cost model assumes that heat is supplied via condensation of saturated steam (see Dutta et al.)
"""
cost_crystallizer_by_crystal_mass(blk)
def _cost_crystallizer_flows(blk):
blk.costing_package.cost_flow(
pyo.units.convert(
(blk.unit_model.heat_required / _compute_steam_properties(blk)),
to_units=pyo.units.m**3 / pyo.units.s,
),
"steam",
)
[docs]@register_costing_parameter_block(
build_rule=build_surrogate_crystallizer_cost_param_block,
parameter_block_name="surrogate_crystallizer",
)
def cost_crystallizer_by_crystal_mass(blk):
"""
Mass-based capital cost for FC crystallizer
"""
make_capital_cost_var(blk)
blk.costing_package.add_cost_factor(blk, "TIC")
blk.cost_factor = 1 # blk.costing_package.add_cost_factor(blk, "TIC")
blk.capital_cost_constraint = pyo.Constraint(
expr=blk.capital_cost
== blk.cost_factor
* pyo.units.convert(
(
blk.costing_package.surrogate_crystallizer.iec_percent
* blk.costing_package.surrogate_crystallizer.fob_unit_cost
* (
blk.unit_model.flow_mass_sol_total
/ blk.costing_package.surrogate_crystallizer.ref_capacity
)
** blk.costing_package.surrogate_crystallizer.ref_exponent
),
to_units=blk.costing_package.base_currency,
)
)
_cost_crystallizer_flows(blk)
def _compute_steam_properties(blk):
"""
Function for computing saturated steam properties for thermal heating estimation.
Args:
pressure_sat: Steam gauge pressure in bar
Out:
Steam thermal capacity (latent heat of condensation * density) in kJ/m3
"""
pressure_sat = blk.costing_package.surrogate_crystallizer.steam_pressure
# 1. Compute saturation temperature of steam: computed from El-Dessouky expression
tsat_constants = [
42.6776 * pyo.units.K,
-3892.7 * pyo.units.K,
1000 * pyo.units.kPa,
-9.48654 * pyo.units.dimensionless,
]
psat = (
pyo.units.convert(pressure_sat, to_units=pyo.units.kPa)
+ 101.325 * pyo.units.kPa
)
temperature_sat = tsat_constants[0] + tsat_constants[1] / (
pyo.log(psat / tsat_constants[2]) + tsat_constants[3]
)
# 2. Compute latent heat of condensation/vaporization: computed from Sharqawy expression
t = temperature_sat - 273.15 * pyo.units.K
enth_mass_units = pyo.units.J / pyo.units.kg
t_inv_units = pyo.units.K**-1
dh_constants = [
2.501e6 * enth_mass_units,
-2.369e3 * enth_mass_units * t_inv_units**1,
2.678e-1 * enth_mass_units * t_inv_units**2,
-8.103e-3 * enth_mass_units * t_inv_units**3,
-2.079e-5 * enth_mass_units * t_inv_units**4,
]
dh_vap = (
dh_constants[0]
+ dh_constants[1] * t
+ dh_constants[2] * t**2
+ dh_constants[3] * t**3
+ dh_constants[4] * t**4
)
dh_vap = pyo.units.convert(dh_vap, to_units=pyo.units.kJ / pyo.units.kg)
# 3. Compute specific volume: computed from Affandi expression (Eq 5)
t_critical = 647.096 * pyo.units.K
t_red = temperature_sat / t_critical # Reduced temperature
sp_vol_constants = [
-7.75883 * pyo.units.dimensionless,
3.23753 * pyo.units.dimensionless,
2.05755 * pyo.units.dimensionless,
-0.06052 * pyo.units.dimensionless,
0.00529 * pyo.units.dimensionless,
]
log_sp_vol = (
sp_vol_constants[0]
+ sp_vol_constants[1] * (pyo.log(1 / t_red)) ** 0.4
+ sp_vol_constants[2] / (t_red**2)
+ sp_vol_constants[3] / (t_red**4)
+ sp_vol_constants[4] / (t_red**5)
)
sp_vol = pyo.exp(log_sp_vol) * pyo.units.m**3 / pyo.units.kg
# 4. Return specific energy: density * latent heat
return dh_vap / sp_vol