Engineering task and calculation objective
The NaOH module delivers the physical properties of aqueous sodium hydroxide solutions (caustic soda) as a function of temperature and concentration. The range of validity covers 20 °C to 100 °C and 0 to 50 wt% NaOH – covering the range in which caustic soda is typically handled, stored and concentrated in the chemical, pulp and paper, food and water treatment industries.
Calculated properties are density, saturation pressure, specific heat capacity, thermal conductivity, dynamic and kinematic viscosity, as well as the derived quantities Prandtl number, coefficient of thermal expansion and thermal diffusivity. Anyone who wants to calculate the density of caustic soda, determine the viscosity of a 50 % lye for pump sizing, or design the heat transfer in a caustic cooler will find all required input data here, consistently from a single data set.
The strong concentration dependence is decisive: concentrated caustic soda is considerably denser and more viscous than water, its vapour pressure is significantly depressed (boiling point elevation) and its heat capacity is reduced. Calculations using water properties therefore lead to gross errors in pressure drop, heat transfer and evaporator design for lye.
Calculation workflow
- Define the state: Temperature (20 °C to 100 °C) and NaOH concentration (0 to 50 wt%) are entered. The module checks whether the state lies within the range of validity of the stored correlations.
- Evaluate the basic properties: From the correlations, density, specific heat capacity, thermal conductivity and dynamic viscosity of the solution are calculated as functions of both state variables; in addition, the saturation pressure of the solution is determined, which is depressed relative to pure water as a function of concentration.
- Form derived quantities: From the basic values follow the kinematic viscosity (η/ρ), the Prandtl number (η·cp/λ), the thermal diffusivity (λ/(ρ·cp)) and the coefficient of thermal expansion from the temperature dependence of the density.
- Transfer the values into the process calculation: The properties feed into downstream design tasks: Reynolds number and pressure drop of piping and pumps, Nusselt correlations for heat exchangers, and boiling and evaporation calculations via the saturation pressure.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Temperature | ϑ1 ϑ2 | °C |
| Temperature | ϑ1 ϑ2 | °C |
| Concentration | c1 c2 | Ma-% |
| Concentration | c1 c2 | Ma-% |
| 1 | (20 °C) c1 c2 | g/l |
| 2 | (20 °C) c1 c2 | g/l |
| 1 | c1 c2 | mol/l |
| 2 | c1 c2 | mol/l |
| Density | ρ1 ρ2 | kg/m³ |
| Density | ρ1 ρ2 | kg/m³ |
| Specific heat capacity | cp1 cp2 | J/(kg·K) |
| Specific heat capacity | cp1 cp2 | J/(kg·K) |
| Dynamic viscosity | η1 η2 | mPa·s |
| Dynamic viscosity | η1 η2 | mPa·s |
| Saturation pressure | pS,1 pS,2 | Pa |
| Saturation pressure | pS,1 pS,2 | Pa |
| Thermal conductivity | λ1 λ2 | W/(m·K) |
| Thermal conductivity | λ1 λ2 | W/(m·K) |
| Kinematic viscosity | ν1 ν2 | m²/s |
| Kinematic viscosity | ν1 ν2 | m²/s |
| Prandtl number | Pr1 Pr2 | - |
| Prandtl number | Pr1 Pr2 | - |
| Coefficient of thermal expansion | β1 β2 | 1/K |
| Coefficient of thermal expansion | β1 β2 | 1/K |
Frequently asked questions
Why is the saturation pressure of the lye lower than that of pure water?
Dissolved NaOH lowers the water activity of the solution; with increasing concentration, the vapour pressure drops well below the pure-water value. In practice, this means a boiling point elevation: a 50 % lye boils at atmospheric pressure only well above 100 °C. For evaporators, this means the usable temperature difference shrinks by the boiling point elevation.
How strongly does the viscosity change with concentration?
Very strongly and non-linearly: while dilute lye flows almost like water, concentrated caustic soda at room temperature is many times more viscous than water. Since the viscosity at the same time drops strongly with temperature, pump and heat transfer calculations must always be carried out with the properties at the actual operating temperature and concentration.
What needs to be considered outside the range of validity?
Below 20 °C, at high concentrations one approaches the crystallisation limit: concentrated caustic soda can crystallise out at temperatures well above 0 °C and block lines – storage tanks and piping for 50 % lye are therefore heated. Above 100 °C and above 50 wt%, the module's correlations are not validated; separate data is required there.
Which concentration measure do the properties refer to?
To the mass fraction of NaOH in the solution (wt%). Confusion with molarity (mol/l) or mass concentration (g/l) is a typical source of error, since large differences arise for lye due to its high density: a 50 wt% lye contains about 763 g of NaOH per litre of solution.