Chemical Softening

This chemical softening model includes the units mixer, flocculator, sedimentation basin and recarbonation basin. The model calculates the chemical dose required for target removal of hardness causing components and calculates the size of the mixer, flocculator, sedimentation basin and the recarbonation basin. This chemical softening model:

supports steady-state only

predicts the outlet concentration of \(\text{Ca}^{2+}\) and \(\text{Mg}^{2+}\)

is verified against literature data

Configuration Inputs

The model requires 2 configuration inputs:

Softening procedure: single_stage_lime or excess_lime or single_stage_lime_soda or excess_lime_soda
Silica removal: True or False

Solution Composition

This chemical softening model requires an input solute list from the user. Components that must be included are shown in the code below. Additional components can be included by the user such as TDS. The MCAS property package is used in this chemical softening model.

component_list = ["Ca_2+","Mg_2+","Alkalinity_2-"]

A default removal efficiency is assumed for components (other than \(\text{Ca}^{2+}\) and \(\text{Mg}^{2+}\)) and shown below in the code block.

removal_eff_dict = dict(
         zip([
             x for x in component_list if x not in ["Ca_2+","Mg_2+"]
             ]
             ,
             [
                 0.7 if j != "TDS" else 1e-3
                 for j in component_list
             ],
         )
     )

Users can update the removal efficiencies for specific components by first fixing the removal_efficiency variable and then using the specific component as a key to modify its removal efficiency as shown below.

removal_efficiency.fix()
removal_efficiency['Cl_-'].fix(0.8)

Degrees of Freedom/Variables

The chemical softening model has 18 degrees of freedom that should be fixed for the unit to be fully specified. Additionally, depending on the chemical softening process selected, chemical dosing may or may not be required to be fixed.

Typically, the following 7 variables define the input feed.

Variables	Variable Name	Symbol	Unit
Feed volume flow rate	`properties_in[0].flow_mass_phase_comp['Liq','H2O']`	\(Q_{feed}\)	\(\text{m}^3 / \text{s}\)
Feed composition Ca2+	`properties_in[0].flow_mass_phase_comp['Liq','Ca_2+']`	\(m_{Ca^{2+}}\)	\(\text{g/}\text{L}\)
Feed composition Mg2+	`properties_in[0].flow_mass_phase_comp['Liq','Mg_2+']`	\(m_{Mg^{2+}}\)	\(\text{g/}\text{L}\)
Feed composition Alkalinity2-	`properties_in[0].flow_mass_phase_comp['Liq','Alkalinity_2-']`	\(m_{alk}\)	\(\text{g/}\text{L}\)
Feed temperature	`feed_props.temperature`	\(T\)	\(^o\text{C}\)
Ca2+ effluent target in CaCO3 equivalents	`ca_eff_target`		\(\text{g/}\text{L}\)
Mg2+ effluent target in CaCO3 equivalents	`mg_eff_target`		\(\text{g/}\text{L}\)

The following 11 variables define the system design.

Variables	Variable Name	Symbol	Valid Range	Unit
Number of mixers	`no_of_mixer`	\(n_{mixer}\)		\(\text{dimensionless}\)
Number of flocculators	`no_of_floc`	\(n_{floc}\)		\(\text{dimensionless}\)
Retention time of mixer	`retention_time_mixer`	\(RT_{mixer}\)	0.1-5	\(\text{min}\)
Retention time of flocculator	`retention_time_floc`	\(RT_{floc}\)	10-45	\(\text{min}\)
Retention time of sedimentation basin	`retention_time_sed`	\(RT_{sed}\)	120-240	\(\text{min}\)
Retention time of recarbonation basin	`retention_time_recarb`	\(RT_{recarb}\)	15-30	\(\text{min}\)
Fractional volume recovery	`frac_vol_recovery`			\(\text{dimensionless}\)
Removal efficiency of components (except Ca2+ and Mg2+)	`removal_efficiency`			\(\text{dimensionless}\)
CO2 dose in CaCO3 equivalents	`CO2_CaCO3`	\(CO_{2,CaCO_{3}-hardness}\)		\(\text{g/}\text{L}\)
Velocity gradient in mixer	`vel_gradient_mix`	\(\text{velocity gradient}_{mixer}\)	300-1000	\(\text{/}\text{s}\)
Velocity gradient in flocculator	`vel_gradient_floc`	\(\text{velocity gradient}_{floc}\)	20-80	\(\text{/}\text{s}\)

The following variables should be fixed to 0 if their dose is not calculated in the softening procedure for the model to be fully specified. The softening procedure where the doses are calculated in are listed in the table.

Variables	Softening procedure	Variable Name	Symbol	Unit
Excess lime	excess_lime, excess_lime_soda	`excess_CaO`	\(CaO\)	\(\text{g/}\text{L}\)
Soda ash	single_stage_lime_soda, excess_lime_soda	`Na2CO3_dosing`	\(Na_{2}CO_{3}\)	\(\text{g/}\text{L}\)
CO2 dose in second basin	excess_lime_soda	`CO2_second_basin`	\(CO_{2,second-basin}\)	\(\text{g/}\text{L}\)
MgCl2	Silica removal	`MgCl2_dosing`	\(MgCl_{2}\)	\(\text{g/}\text{L}\)

Model Structure

This chemical softening model consists of 3 StateBlocks (as 3 Ports in parenthesis below).

Inlet (inlet)
Outlet (outlet)
Waste (waste)

The softening procedure type and whether or not silica removal is desired is set up in the configuration of the unit block.

Sets

The components \(\text{Ca}^{2+}\), \(\text{Mg}^{2+}\) and \(\text{Alkalinity}^{2-}\) must be included in the components.

Description	Symbol	Indices
Time	\(t\)	[0]
Phases	\(p\)	[‘Liq’, ‘Vap’]
Components	\(j\)	[‘H2O’, ‘Ca_2+’, ‘ Mg_2+’, ‘Alkalinity_2-‘]

Parameters

The following parameters are used as default values and are not mutable.

Description	Parameter Name	Symbol
Ratio of MgCl2 to SiO2	`MgCl2_SiO2_ratio`	\(Ratio_{MgCl_{2}/SiO_{2}}\)
Sludge produced per kg Ca in CaCO3 hardness	`Ca_hardness_CaCO3_sludge_factor`	\(\text{Ca-SF}_{CaCO_{3}-hardness}\)
Sludge produced per kg Mg in CaCO3 hardness	`Mg_hardness_CaCO3_sludge_factor`	\(\text{Mg-SF}_{CaCO_{3}-hardness}\)
Sludge produced per kg Mg in non-CaCO3 hardness	`Mg_hardness_nonCaCO3_sludge_prod_factor`	\(\text{Mg-SF}_{non-CaCO_{3}-hardness}\)
Multiplication factor to calculate excess CaO	`excess_CaO_coeff`

Equations

The chemical dose is calculated based on the type of softening procedure selected in the configuration of the flowsheet.

Single Stage Lime
Description	Equation
Lime dose	Carbonic acid concentration + Calcium carbonate hardness
Soda ash dose	None
Carbon dioxide first stage	Alkalinity - Calcium hardness + Residual calcium hardness

Excess Lime
Description	Equation
Lime dose	Carbonic acid concentration + Total alkalinity + Magnesium hardness + Excess lime dose
Soda ash dose	None
Carbon dioxide first stage	Alkalinity - Total hardness + Residual calcium hardness + Residual magnesium hardness

Single Stage Lime-Soda Ash
Description	Equation
Lime dose	Carbonic acid concentration + Calcium carbonate hardness
Soda ash dose	Calcium non-carbonate hardness and/or Magnesium non-carbonate hardness
Carbon dioxide first stage	Alkalinity + Soda ash dose - Calcium hardness + Residual calcium hardness

Excess Lime-Soda Ash
Description	Equation
Lime dose	Carbonic acid concentration + Calcium carbonate hardness + 2*Magnesium hardness + Magnesium non-carbonate hardness + Excess lime
Soda ash dose	Calcium non-carbonate hardness + Magnesium non-carbonate hardness
Carbon dioxide first stage	Lime dose + Residual magnesium hardness
Carbon dioxide second stage	Alkalinity + Soda ash dose - Source total hardness + Residual hardness

The following equations are independent of the softening procedure selected but depend on the feed composition.

Description	Variable Name	Symbol	Equation
MgCl2 dose (if silica removal is selected)	`mgcl2_dosing`	\(MgCl_{2}\)	\(Ratio_{MgCl_{2}/SiO_{2}} * SiO_{2}\)
Sludge produced	`sludge_prod`	\(m_{sludge}\)	\(Q_{feed} * (\text{Ca-SF}_{CaCO_{3}-hardness} * Ca_{CaCO_{3}-hardness} + \text{Mg-SF}_{CaCO_{3}-hardness} * Mg_{CaCO_{3}-hardness} + Ca_{non-CaCO_{3}-hardness} + \text{Mg-SF}_{non-CaCO_{3}-hardness} * Mg_{non-CaCO_{3}-hardness} + \text{Excess CaO} + TSS + MgCl_{2})\)
Volume of mixer	`volume_mixer`	\(V_{mixer}\)	\(Q_{feed} * RT_{mixer} * n_{mixer}\)
Volume of flocculator	`volume_floc`	\(V_{floc}\)	\(Q_{feed} * RT_{floc} * n_{floc}\)
Volume of sedimentation basin	`volume_sed`	\(V_{sed}\)	\(Q_{feed} * RT_{sed}\)
Volume of recarbonation basin	`volume_recarb`	\(V_{recarb}\)	\(Q_{feed} * RT_{recarb}\)

Costing

The following table lists out the coefficients used in the cost equations to calculate the capital and operating costs for the mixer, flocculator, sedimentation basin and recarbonation basin [7,8]. The coefficients are assigned as mutable Parameters.

Unit	Variable Name	`_constant`	`_coeff/_coeff_1`	`_coeff_2`	`_coeff_3`	`_exp/_exp_1`	`_exp_2`
Capital
Mixer	`mix_tank_capital`	28584	0.0002	22.776		2
Flocculator	`floc_tank_capital`	217222	673894
Sedimentation basin	`sed_basin_capital`	182801	-0.0005	86.89		2
Recarbonation basin	`recarb_basin_capital`	19287	4e-9	-0.0002	10.027	3	2
Recarbonation basin source	`recarb_basin_source_capital`	130812	9e-8	-0.001	42.578		2
Lime feed system	`lime_feed_system_capital`	193268	20.065
Administrative capital	`admin_capital`		69195			0.5523
Operating
Mixer	`mix_tank_op`	22588	-3e-8	0.0008	2.8375	3	2
Flocculator	`floc_tank_op`	6040	3e-13	-4e-7	0.318	3	2
Sedimentation basin	`sed_basin_op`	6872	7e-10	-0.00005	1.5908	3	2
Recarbonation basin	`recarb_basin_op`	10265	1e-8	-0.0004	6.19	3	2
Lime feed system	`lime_feed_system_op`		4616.7			0.4589
Lime sludge management system	`sludge_disposal_cost`		35
Administrative Operational	`admin_op`		88589			0.4589

The following equations are used to calculate the components of the capital costs for the mixer, flocculator, sedimentation basin and recarbonation basin units and other costs.

Unit	Equation
Mixer	\(\text{Capital Cost}_{mixer} = (0.0002 * V_{mixer})^{2} + (22.776 * V_{mixer}) + 28584\)
Flocculator	\(\text{Capital Cost}_{floc} = (673894 * V_{floc}) + (C_2 * V_{floc}) + 217222\)
Sedimentation basin	\(\text{Capital Cost}_{sed} = (-0.0005 * V_{sed}/Depth_{sed})^{2} + (86.89 * V_{mixer}/Depth_{sed}) + 182801\)
Recarbonation basin	\(\text{Capital Cost}_{recarb} = (4e-9 * V_{recarb})^{3} + (-0.0002 * V_{recarb})^{2} + (10.027 * V_{recarb}) + 19287\)
Recarbonation source basin	\(\text{Capital Cost}_{recarb_source} = (9e-8 * (CO_{2,first-basin} + CO_{2,second-basin})) + (-0.001 * (CO_{2,first-basin} + CO_{2,second-basin})){2} + (42.578 * (CO_{2,first-basin} + CO_{2,second-basin})) + 130812\)
Lime feed system	\(\text{Capital Cost}_{lime} = (20.065 * CaO) + 193268\)
Administrative	\(\text{Capital Cost}_{admin} = (69195 * Q_{feed})^{0.5523}\)

The following equations are used to calculate the components of the operating costs for the mixer, flocculator, sedimentation basin and recarbonation basin units and other costs.

Unit	Equation
Mixer	\(\text{Operating Cost}_{mixer} = (-3e-8 * V_{mixer})^{3} + (0.0008* V_{mixer})^{2} + (2.8375 * V_{mixer}) + 22588\)
Flocculator	\(\text{Operating Cost}_{floc} = (3e-13 * V_{floc})^{3} + (-4e-7 * V_{floc})^{2} + (0.318 * V_{floc}) + 6040\)
Sedimentation basin	\(\text{Operating Cost}_{sed} = (7e-10 * V_{sed}/Depth_{sed})^{3} + (-0.00005 * V_{mixer}/Depth_{sed})^{2} + (1.5908 * V_{mixer}/Depth_{sed}) + 6872\)
Recarbonation basin	\(\text{Operating Cost}_{recarb} = (1e-8* V_{recarb})^{3} + (-0.0004 * V_{recarb})^{2} + (6.19 * V_{recarb}) + 10265\)
Lime feed system	\(\text{Operating Cost}_{lime} = (4616.7 * CaO)^{0.4589}\)
Lime sludge management	\(\text{Operating Cost}_{lime-sludge} = (35 * m_{sludge})\)
Administrative	\(\text{Operating Cost}_{admin} = (88589 * Q_{feed})^{0.4589}\)

The following equations are used to calculate the power consumption by the mixer and the flocculator used to calculate total electricity consumption.

Unit	Equation
Mixer	\(Power_{mixer} = \text{velocity gradient}_{mixer}^{2} * V_{mixer} * viscosity\)
Flocculator	\(Power_{floc} = \text{velocity gradient}_{floc}^{2} * V_{floc} * viscosity\)

References

[1] Crittenden, J. C., & Montgomery Watson Harza (Firm). (2012). Water treatment principles and design. Hoboken, N.J: J.Wiley.

[2] Davis, M. L. (2010). Water and wastewater engineering: Design principles and practice.

[3] Baruth. (2005). Water treatment plant design / American Water Works Association, American Society of Civil Engineers; Edward E. Baruth, technical editor. (Fourth edition.). McGraw-Hill.

[4] Edzwald, J. K., & American Water Works Association. (2011). Water quality & treatment: A handbook on drinking water. New York: McGraw-Hill.

[5] R.O. Mines Environmental Engineering: Principles and Practice, 1st Ed, John Wiley & Sons

[6] Lee, C. C., & Lin, S. D. (2007). Handbook of environmental engineering calculations. New York: McGraw Hill.

[7] Sharma, J.R. (2010). Development Of a Preliminary Cost Estimation Method for Water Treatment Plants

[8] McGivney, W. T. & Kawamura, S. (2008) Cost Estimating Manual for Water Treatment Facilities. John Wiley & Sons, Inc., Hoboken, NJ, USA.