Skip to content

Latest commit

 

History

History
133 lines (103 loc) · 5.73 KB

coagulation.rst

File metadata and controls

133 lines (103 loc) · 5.73 KB
Raw

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 M_j flow_mass_phase_comp [p, j] \text{kg/s}
Temperature T temperature None \text{K}
Pressure P pressure None \text{Pa}

Parameters

Description Symbol Parameter Index Units
Fluid specific heat capacity c_p cp None \text{J/kg/K}
Reference density (at 273 K) \rho_{ref} ref_dens_liq None \text{kg/}\text{m}^3
Relative density contribution from salt mass fraction \rho_s dens_slope None \text{kg/}\text{m}^3
First density temperature coefficient A dens_param_A None \text{K}^{-2}
Second density temperature coefficient B dens_param_B None \text{K}^{-1}
Third density temperature coefficient C dens_param_C None \text{dimensionless}
First pressure coefficient \alpha ref_pressure_correction None \text{dimensionless}
Second pressure coefficient \beta ref_pressure_slope None \text{Pa}^{-1}
Reference viscosity (at 273 K) \mu_{ref} mu_A None \text{kg/}\text{m/}\text{s}
First viscosity temperature coefficient \mu_B mu_B None \text{K}
Second viscosity temperature coefficient \mu_C mu_C None \text{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 x_j mass_frac_phase_comp [p, j] \text{dimensionless}
Mass density of fluid \rho dens_mass_phase [p] \text{kg/}\text{m}^3
Phase volumetric flowrate Q_p flow_vol_phase [p] \text{m}^3\text{/s}
Mass concentration C_j conc_mass_phase_comp [p, j] \text{kg/}\text{m}^3
Dynamic viscosity \mu visc_d_phase [p] \text{Pa}\cdotp\text{s}
Enthalpy flow H enth_flow None \text{J/s}

Relationships

Description Equation
Component mass fraction x_j = \frac{M_j}{\sum_{j} M_j}
Mass density \rho = (\rho_{ref} + \rho_s \cdotp \sum_{j} x_j) \cdotp (A \cdotp T^2 + B \cdotp T + C) \cdotp (\alpha + \beta \cdotp P)
Volumetric flowrate Q = \frac{\sum_{j} M_j}{\rho}
Mass concentration C_j = x_j \cdotp \rho
Dynamic viscosity \mu = \mu_{ref} \cdotp exp( \frac{\mu_B}{T - \mu_C} )
Enthalpy flow H = c_p \cdotp \sum_{j} M_j \cdotp (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:

.. testsetup::

  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(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)