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Coagulation Property Package

This package implements property relationships for water density as a function of temperature, pressure, and mass fraction of suspended/dissolved solids from Engineering Toolbox. (2003) and water viscosity as a function of temperature from D.S. Viswananth, G. Natarajan. (1989).

Note: TDS = Total Dissolved Solids and TSS = Total Suspended Solids

This coagulation property package:
  • supports only 'H2O', 'TDS', 'TSS', and 'Sludge' as Components
  • supports only liquid phase
  • is formulated on a mass basis
  • does NOT support formulations on a molar basis
  • includes mass density correction for fraction of suspended/dissolved solids

Sets

Description Symbol Indices
Components j ['H2O', 'TDS', 'TSS', 'Sludge']
Phases p ['Liq']

State variables

Description Symbol Variable Index Units
Component mass flowrate Mj flow_mass_phase_comp [p, j] kg/s
Temperature T temperature None K
Pressure P pressure None Pa

Parameters

Description Symbol Parameter Index Units
Fluid specific heat capacity cp cp None J/kg/K
Reference density (at 273 K) ρref ref_dens_liq None kg/m3
Relative density contribution from salt mass fraction ρs dens_slope None kg/m3
First density temperature coefficient A dens_param_A None K − 2
Second density temperature coefficient B dens_param_B None K − 1
Third density temperature coefficient C dens_param_C None dimensionless
First pressure coefficient α ref_pressure_correction None dimensionless
Second pressure coefficient β ref_pressure_slope None Pa − 1
Reference viscosity (at 273 K) μref mu_A None kg/m/s
First viscosity temperature coefficient μB mu_B None K
Second viscosity temperature coefficient μC mu_C None K

The parameters provided are valid between 0 and 350 °C and up to 600 bar.

Properties

Description Symbol Variable Index Units
Component mass fraction xj mass_frac_phase_comp [p, j] dimensionless
Mass density of fluid ρ dens_mass_phase [p] kg/m3
Phase volumetric flowrate Qp flow_vol_phase [p] m3/s
Mass concentration Cj conc_mass_phase_comp [p, j] kg/m3
Dynamic viscosity μ visc_d_phase [p] Pa · s
Enthalpy flow H enth_flow None J/s

Relationships

Description Equation
Component mass fraction $x_j = \frac{M_j}{\sum_{j} M_j}$
Mass density ρ = (ρref + ρs · ∑jxj) · (A · T2 + B · T + C) · (α + β · P)
Volumetric flowrate $Q = \frac{\sum_{j} M_j}{\rho}$
Mass concentration Cj = xj · ρ
Dynamic viscosity $\mu = \mu_{ref} \cdotp exp( \frac{\mu_B}{T - \mu_C} )$
Enthalpy flow H = cp · ∑jMj · (T − 273)

Scaling

This coagulation property package includes support for scaling, such as providing default or calculating scaling factors for almost all variables. The only variables that do not have scaling factors are the component mass flowrate and the user will receive a warning if these are not set.

The user can specify the scaling factors for component mass flowrates with the following:

from pyomo.environ import ConcreteModel from idaes.core import FlowsheetBlock

# relevant imports import watertap.property_models.coagulation_prop_pack as props from idaes.core.util.scaling import calculate_scaling_factors

# relevant assignments m = ConcreteModel() m.fs = FlowsheetBlock(default={"dynamic": False}) m.fs.properties = props.CoagulationParameterBlock()

# set scaling for component mass flowrate m.fs.properties.set_default_scaling('flow_mass_phase_comp', 1, index=('Liq','H2O')) m.fs.properties.set_default_scaling('flow_mass_phase_comp', 1e2, index=('Liq','TDS')) m.fs.properties.set_default_scaling('flow_mass_phase_comp', 1e2, index=('Liq','TSS')) m.fs.properties.set_default_scaling('flow_mass_phase_comp', 1e3, index=('Liq','Sludge'))

# calculate scaling factors calculate_scaling_factors(m.fs)

The default scaling factors are as follows:

  • 1e-2 for temperature
  • 1e-6 for pressure
  • 1e-3 for mass density
  • 1e3 for dynamic viscosity

Scaling factors for other variables can be calculated based on their relationships with the user-supplied or default scaling factors.

Reference

Engineering Toolbox. Water - Density, Specific Weight, and Thermal Expansion Coefficients. (2003) https://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html [Accessed 02-01-2022]

D.S. Viswananth, G. Natarajan. Data Book on the Viscosity of Liquids. Hemisphere Publishing Corp. (1989)