Ion Exchange Costing Method

Costing Method Parameters

The following parameters are constructed for the unit on the FlowsheetCostingBlock (e.g., m.fs.costing.ion_exchange) when applying the cost_ion_exchange costing method in the watertap_costing_package:

Description	Symbol	Parameter Name	Default Value	Units	Notes
Anion exchange resin cost	\(c_{res,ax}\)	anion_exchange_resin_cost	205	\(\text{USD}_{2020}\text{/ft}^{3}\)	Assumes strong base polystyrenic gel-type Type II. From EPA-WBS cost model.
Cation exchange resin cost	\(c_{res,cx}\)	cation_exchange_resin_cost	153	\(\text{USD}_{2020}\text{/ft}^{3}\)	Assumes strong acid polystyrenic gel-type. From EPA-WBS cost model.
Regenerant dose per volume of resin	\(D_{regen}\)	regen_dose	300	\(\text{kg/}\text{m}^{3}\)	Mass of regenerant chemical per cubic meter of resin volume
Ion exchange column cost equation A coeff	\(C_{col,A}\)	vessel_A_coeff	1596.499	\(\text{USD}_{2020}\)	Carbon steel w/ stainless steel internals. From EPA-WBS cost model.
Ion exchange column cost equation B coeff	\(C_{col,b}\)	vessel_b_coeff	0.459496	\(\text{dimensionless}\)	Carbon steel w/ stainless steel internals. From EPA-WBS cost model.
Backwash/rinse tank cost equation A coeff	\(C_{bw,A}\)	backwash_tank_A_coeff	308.9371	\(\text{USD}_{2020}\)	Steel tank. From EPA-WBS cost model.
Backwash/rinse tank cost equation B coeff	\(C_{bw,b}\)	backwash_tank_b_coeff	0.501467	\(\text{dimensionless}\)	Steel tank. From EPA-WBS cost model.
Regeneration solution tank cost equation A coeff	\(C_{regen,A}\)	regen_tank_A_coeff	57.02158	\(\text{USD}_{2020}\)	Stainless steel tank. From EPA-WBS cost model.
Regeneration solution tank cost equation B coeff	\(C_{regen,b}\)	regen_tank_b_coeff	0.729325	\(\text{dimensionless}\)	Stainless steel tank. From EPA-WBS cost model.
Fraction of resin replaced per year	\(f_{res}\)	annual_resin_replacement_factor	0.05	\(1/\text{yr}\)	Estimated 4-5% per year. From EPA-WBS cost model.
Minimum hazardous waste disposal cost	\(c_{haz,min}\)	hazardous_min_cost	3240	\(\text{USD}_{2020}\text{/yr}\)	Minimum cost per hazardous waste shipment. From EPA-WBS cost model.
Unit cost for hazardous waste resin disposal	\(c_{haz,res}\)	hazardous_resin_disposal	347.10	\(\text{USD}_{2020}\text{/ton}\)	From EPA-WBS cost model.
Unit cost for hazardous waste regeneration solution disposal	\(c_{haz,regen}\)	hazardous_regen_disposal	3.64	\(\text{USD}_{2020}\text{/gal}\)	From EPA-WBS cost model.
Number of cycles the regenerant can be reused before disposal	\(n_{recycle}\)	regen_recycle	1	\(\text{dimensionless}\)	Can optionally be set by the user to investigate more efficient regen regimes.
Costing factor to account for total installed cost installation of equipment	\(f_{TIC}\)	total_installed_cost_factor	1.65	\(\text{dimensionless}\)	Costing factor to account for total installed cost of equipment
Unit cost of regenerant	\(c_{regen}\)	Regenerant dependent; see table below	Regenerant dependent; see table below	Regenerant dependent; see table below	Regenerant dependent; see table below

The unit cost of regenerant is dependent on the type of regenerant used in the unit model configuration. These parameters are created directly on m.fs.costing.

Description	Parameter Name	Default Value	Units	Notes
Unit cost of NaCl	nacl	0.09	\(\text{USD}_{2020}\text{/kg}\)	Assumes solid NaCl. From CatCost v 1.0.4
Unit cost of HCl	hcl	0.17	\(\text{USD}_{2020}\text{/kg}\)	Assumes 37% solution HCl. From CatCost v 1.0.4
Unit cost of NaOH	naoh	0.59	\(\text{USD}_{2020}\text{/kg}\)	Assumes 30% solution NaOH. From iDST
Unit cost of Methanol (MeOH)	meoh	3.395	\(\text{USD}_{2008}\text{/kg}\)	Assumes 100% pure MeOH. From ICIS

Costing Method Variables

The following variables are constructed on the unit block (e.g., m.fs.unit.costing) when applying the cost_ion_exchange costing method in the watertap_costing_package:

Description	Symbol	Variable Name	Index	Units
Density of regenerant solution	\(\rho_{regen}\)	regen_soln_dens	None	\(\text{kg/}\text{m}^{3}\)
Regenerant dose required for regeneration per volume of resin [kg regenerant/m3 resin]	\(D_{regen}\)	regen_dose	None	\(\text{kg/}\text{m}^{3}\)
Capital cost for one vessel	\(C_{col}\)	capital_cost_vessel	None	\(\text{USD}\)
Capital cost for resin for one vessel	\(C_{resin}\)	capital_cost_resin	None	\(\text{USD}\)
Capital cost for regeneration solution tank	\(C_{regen}\)	capital_cost_regen_tank	None	\(\text{USD}\)
Capital cost for backwash + rinse solution tank	\(C_{bw}\)	capital_cost_backwash_tank	None	\(\text{USD}\)
Operating cost for hazardous waste disposal	\(D_{regen}\)	operating_cost_hazardous	None	\(\text{USD/}\text{yr}\)
Regeneration solution flow	\(\dot{v}_{regen}\)	flow_mass_regen_soln	None	\(\text{kg/}\text{yr}\)
Total pumping power required	\(P_{tot}\)	total_pumping_power	None	\(\text{kW}\)

Capital Cost Calculations

Capital costs for ion exchange in the watertap_costing_package are the summation of the total cost of the resin, columns, backwashing tank, and regeneration solution tank:

Resin is costed based on the total volume of resin required for the system, where \(c_{res}\) is the cost per volume of resin (either cation, \(c_{res,cx}\), or anion exchange resin, \(c_{res,ax}\)):

\[C_{resin} = V_{res,tot} c_{res}\]

Vessel cost as a function of volume was fit to a power function to determine capital cost of each column:

\[C_{col} = C_{col,A} V_{col}^{C_{col,b}}\]

The backwashing tank is assumed to include backwash and rinsing volumes. The total volume of this tank is:

\[V_{bw} = Q_{bw} t_{bw} + Q_{rinse} t_{rinse}\]

Backwashing tank cost as a function of volume was fit to a power function to determine capital cost of the backwashing tank:

\[C_{bw} = C_{bw,A} V_{bw}^{C_{bw,b}}\]

Regeneration tank cost as a function of volume was fit to a power function to determine capital cost of the regeneration tank:

\[C_{regen} = C_{regen,A} V_{regen}^{C_{regen,b}}\]

And the total capital cost for the ion exchange system is the summation of these:

\[C_{tot} = ((C_{resin} + C_{col}) (n_{op} + n_{red}) + C_{bw} + C_{regen}) f_{TIC}\]

A total installed cost (\(f_{TIC}\)) factor of 1.65 is applied to account for installation costs.

Note

If using single_use option for regenerant configuration keyword, the capital for the regeneration tank is zero.

Operating Cost Calculations

The operating costs for ion exchange includes the annual resin replacement cost, regeneration solution flow, energy consumption for booster pumps, and any hazardous waste handling costs.

Generally, the largest operating cost is the cost of the regeneration solution. The type of regeneration solution used is set via the optional model configuration keyword regenerant. Costing data is available for the following regenerant chemicals:

• NaCl

• HCl

• NaOH

• MeOH

If the user does not provide a value for this option, the model defaults to a NaCl regeneration solution. The dose of regenerant needed is set by the parameter regen_dose in kg regenerant per cubic meter of resin volume. The mass flow of regenerant solution [kg/yr] is:

\[\dot{m}_{regen} = \frac{D_{regen} V_{res} (n_{op} + n_{red})}{t_{cycle} n_{recycle}}\]

Annual resin replacement cost is:

\[C_{op,res} = V_{res} (n_{op} + n_{red}) f_{res} c_{res}\]

If the spent resin and regenerant contains hazardous material, the user designates this by the model configuration keyword hazardous_waste. If set to True, hazardous disposal costs are calculated as a function of the annual mass of resin replaced and regenerant consumed:

\[C_{op,haz} = c_{haz,min} + \bigg( M_{res} (n_{op} + n_{red}) f_{res} \bigg) c_{haz,res} + \dot{v}_{regen} c_{haz,regen}\]

Where \(M_{res}\) is the resin mass for a single bed and \(\dot{v}_{regen}\) is the volumetric flow of regenerant solution. If hazardous_waste is set to False, \(C_{op,haz} = 0\)

The total energy consumed by the unit is the summation of the power required for each of the booster pump, backwashing pump, regeneration pump, and rinsing pump. Each is scaled by the total time required for each step:

\[P_{tot} = \cfrac{P_{main} t_{break} + P_{bw} t_{bw} + P_{regen} t_{regen} + P_{rinse} t_{rinse}}{t_{cycle}}\]

If the user chooses single_use for the regenerant configuration keyword, there is no cost for regeneration solution:

\[\dot{m}_{regen} = \dot{v}_{regen} = 0\]

Instead, the model assumes the entire volume of resin for the operational columns is replaced at the end of each service cycle by calculating the volumetric “flow” of resin:

\[\dot{v}_{resin} = \frac{V_{res, tot}}{t_{break}}\]

And then operational cost of replacing the entire bed is:

\[C_{op,res} = \dot{v}_{resin} c_{res}\]

If hazardous_waste is set to True, the hazardous waste disposal costs are:

\[C_{op,haz} = c_{haz,min} + ( \dot{v}_{resin} \rho_{b} n_{op}) c_{haz,res}\]

Otherwise, \(C_{op,haz} = 0\) as before.

Lastly, the total energy consumed by the unit for single_use configuration includes the booster pump, backwashing pump, and rinsing pump:

\[P_{tot} = \cfrac{P_{main} t_{break} + P_{bw} t_{bw} + P_{rinse} t_{rinse}}{t_{cycle}}\]

Code Documentation

• watertap.costing.unit_models.ion_exchange

References

United States Environmental Protection Agency. (2021). Work Breakdown Structure-Based Cost Models

https://www.epa.gov/sdwa/drinking-water-treatment-technology-unit-cost-models

CatCost https://catcost.chemcatbio.org/

v 1.0.4 available here: https://datahub.chemcatbio.org/dataset/catcost-v1-0-4

Integrated Decision Support Tool (i-DST)

https://idst.mines.edu/