# Species Table - Transport Properties

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# Viscosity

This field is optional and only visible for liquid or gas species.

The unit for Viscosity is Ns/m²

User can use a number formats for entering viscosity data into the SysCAD database:

• Constant - User can enter a constant value
• Equations for Liquid in various forms, see Liquid Viscosity.
• Equation for gases.

NOTE:

1. Some of the equations require data to be entered in specific units. This is generally to match the most commonly available published information. The user may need to convert their data to match the required units of measure.

If viscosity data is added, the individual Species Viscosity data (liquid and gas) can be viewed in SysCAD from the \$SDB window (Species - View Properties).

The stream Viscosity data can be viewed in SysCAD by enabling the Transport Properties group, either by

## Liquid Viscosity

### Liquid Mixture Viscosity

The liquid viscosity ($\displaystyle{ \mu_m }$) is calculated using mass weighted logarithmic mixing:

$\displaystyle{ \mathbf{\mathit{\ln{\mu_m} = \sum{m_i * \ln{\mu_i}}}} }$
Where
 $\displaystyle{ \mu_m }$ = Solution Viscosity $\displaystyle{ \mu_i }$ = Viscosity of component i mi = mass fraction of component i

We can separate water and solutes and describe the liquid viscosity ($\displaystyle{ \mu_m }$) calculation using the water viscosity ($\displaystyle{ \mu_w }$) and the solutes viscosity ($\displaystyle{ \mu_i }$) using following equation:

$\displaystyle{ \mathbf{\mathit{\ln{\mu_m} = m_w * \ln{\mu_w} + \sum{m_i * \ln{\mu_i}}}} }$
Where
 $\displaystyle{ \mu_m }$ = Solution Viscosity $\displaystyle{ \mu_w }$ = Viscosity of water $\displaystyle{ \mu_i }$ = Viscosity of solute i mw = mass fraction of water mi = mass fraction of solute i

The viscosity for each solute ($\displaystyle{ \mu_i }$) can be defined in a number of formats, these are described in the following sections:

### Laliberte´ Viscosity Function

Laliberte_Visc(v1, v2, v3, v4, v5, v6)

The viscosity for each solute ($\displaystyle{ \mu_i }$) is defined by:

$\displaystyle{ \mu_i = \cfrac {e^{\left [ \cfrac{v_1(1-m_w)^{v_2}+v_3}{(v_4*T+1)} \right ]}} {(v_5(1-m_w)^{v_6}+1)} }$

Where

 $\displaystyle{ \mu_i }$ = Viscosity of solute i, mPa.s mw = mass fraction of water mi = mass fraction of solute i T = Temperature in °C v1 to v6 = dimensionless empirical constants.

If the user has appropriate constants for the Laliberte´ equation for aqueous species, then they can select this equation to calculate viscosity as a function of MF & T.

Example

 NaCl(aq): Laliberte_Visc(16.22178863, 1.322930868, 1.48485985, 0.007469126, 30.78020075, 2.058268523):Range(C, 5.0, 154.0)


### Laliberte´ Viscosity Reference and Notes

REFERENCE:

1. Laliberte´ M. Model for Calculating the Viscosity of Aqueous Solutions J. Chem. Eng. Data 2007, 52.

NOTES:

1. The constants for most aqueous species are valid for temperatures between approximately 5 and 120°C.
2. If the unit temperature is outside of the species temperature range, then SysCAD will use the values at the temperature limit.
3. The user MUST define all 6 constants and also the valid range for the function.
4. This method calculates the viscosity of a solution based on ALL of the aqueous species dissolved in the solution. Therefore, if the user wishes to use this method, then it is recommended that all aqueous species in a project use the Laliberte´ method for the results to be consistent.
5. At present, the SysCAD Species database entry does not support the Laliberte Format, user needs to manually specify the equation directly into the data field, thus, do not use the Edit User Data Dialog box via the button.
6. Calculations using the viscosity correlation should be treated as indicative only and use of the numbers in detailed design should be discouraged. Laboratory testing of liquors should be undertaken to provide accurate viscosity measurements for design of equipment.

### Other forms of Liquid Viscosity Equation

Equation Type SysCAD Format General Equation Notes

The most commonly used Liquid Viscosity function is the Andrade equation:

$\displaystyle{ \mu_i = a * e^{b/T} }$

Where:

$\displaystyle{ \mu_i }$ = Viscosity of solute i, mPa.s
a, b, c, d = experimental constants
T = Temperature in Kelvin

Please see Reference literature for values of a, b, c and d.

Andrade equation with 4 term exponential

$\displaystyle{ \mu_i = a * \exp{\left( \frac{b}{T} + c T + d T^2 \right)} }$

Vogel Equation Format

Vogel(a,b,c)

Vogel equation with 3 term exponential

$\displaystyle{ \mu_i = a * \exp{\left( \frac{b}{T-c} \right)} }$

Prausnitz Equation Format The following Prausnitz equation formats are used for entering viscosity data into the SysCAD database:

PrausnitzPow(a,b)

Power equation

$\displaystyle{ \mu_i = a * T^b }$

Prausnitz(a,b)

Modified Andrade equation with 2 term exponential

$\displaystyle{ \ln{\mu_i} = a + \frac{b}{T} }$

$\displaystyle{ \mu_i = \exp \left ( a + \frac{b}{T} \right ) }$

Prausnitz(a,b,c,d)

Modified Andrade equation with 4 term exponential

$\displaystyle{ \ln{\mu_i} = a + \frac{b}{T} + cT + dT^2 }$

$\displaystyle{ \mu_i = \exp \left ( a + \frac{b}{T} + cT + dT^2 \right ) }$

Prausnitz-Vogel Equation Format

PrausnitzVogel(a,b,c)

Prausnitz-Vogel equation with 3 term exponential

$\displaystyle{ \ln{\mu_i} = a + \frac{b}{T+c} }$

$\displaystyle{ \mu_i = \exp{\left(a + \frac{b}{T+c} \right)} }$

REFERENCE:

1. The Properties of Gases and Liquids. Reid & Prausnitz. 4th Edition

NOTES:

1. These equations are generally for “pure liquids” and Temperature range are normally between freezing point to boiling point of the compound.
2. At present, these equations have not be implemented with temperature ranging, user needs to check manually if the stream temperature is within reasonable temperature range.
3. These simple equations are all empirical, they are not reliable and use of the numbers in detailed design should be discouraged. Laboratory testing of liquors should be undertaken to provide accurate viscosity measurements for design of equipment.

### Liquid Viscosity Equation for Alumina Species Model

For users using the Alumina species model, the liquor and slurry viscosity is estimated using in-built equations, see Viscosity.

The calculated viscosity can be viewed in SysCAD by enabling the Transport Properties group, either by

## Gas Viscosity

Constant Simply enter a constant into the field.
Thodos Equation
• Thodos()

# Thermal Conductivity

This field is optional and only visible for liquid or gas species.

The unit for Thermal Conductivity is W/m.K.

User can use a number formats for entering thermal conductivity data into the SysCAD database:

1. Constant - User can enter a constant value
2. Polynomial equation based on temperature
3. Equations for gases based on paper by Misic and Thodos.
• The Misic and Thodos Equation is a function of Cp and T. Other species properties such as molecular weight and critical properties (Tc and Pc) are also used to calculate the thermal conductivity, k, so if Tc or Pc is missing, then species database errors will be given on project load.
• Two equation formats have been implemented in Build138.25032 based on the paper from Misic and Thodos (note unit conversions from original paper);

## Polynomial Format

SysCAD Format General Equation Description / Notes

Poly_TC(C0,C1,C2,C3)

$\displaystyle{ k = C_0 + C_1 T + C_2 T^2 + C_3 T^3 \, }$

where T - Temperature in K

NOTE: The Poly_TC will support up to 4 terms, user can ignore the later constants if the polynomial has less terms.

## Misic and Thodos Equation Formats

SysCAD Format General Equation Description Notes

MisicThodos1()

$\displaystyle{ \left ( \frac {k \lambda} { Cp } \right ) * 10^{4} = \left ( 14.52*T_R - 5.14 \right )^{2/3} }$

$\displaystyle{ k = \left ( \frac {Cp} {\lambda} \right ) * 10^{-4} * \left ( 14.52*T_R - 5.14 \right )^{2/3} }$

Where:

 k = Thermal Conductivity at Normal Pressure (W/m.K) $\displaystyle{ \lambda }$ = $\displaystyle{ \cfrac { T_c^{1/6} * {MW}^{1/2} } { P_c^{2/3} } }$ Cp = heat capacity at constant pressure (kJ/kmol.K) TR = reduced temperature, $\displaystyle{ \frac {T}{T_c} }$ Tc = critical temperature, K. Pc = critical pressure, atm. MW = molecular weight
This equation is suitable for all types of hydrocarbon gases (aliphatic compounds), where the reduced temperature, TR, is between 0.5 and 3.

MisicThodos2()

$\displaystyle{ \left ( \frac {k \lambda} { Cp } \right ) = 0.445 * 10^{-3} * T_R }$

$\displaystyle{ k = \left ( \frac {Cp} {\lambda} \right ) * 0.445 * 10^{-3} * T_R }$

This equation is suitable for methane, naphthene and aromatics gases, where the reduced temperature, TR, is below 1.

Reference:

1. "The Thermal Conductivity of Hydrocarbon Gases at Normal Pressure" - Dragoslav Misic and George Thodos. A.I.Ch.E Journal, pp264, June 1961