Thermodynamics

In Dyssol, thermodynamic functions are applied to calculate a material stream / holdup temperature $T$ from a given enthalpy value $H$ . In most cases, the enthalpy of a compound correlates with temperature non-linearly. Thus, for backward calculation of the temperature from an enthalpy value, you need to solve a non-linear equation $T = f^{-1}(H)$ .

This solving step is replaced by a lookup table functionality, i.e. co-dependent temperature and enthalpy are pre-calculated for a certain range of values and then stored in a table. This table can be used to determine temperature-enthalpy value pairs by interpolation between two neighbor points.

To add more functionality, these lookup tables can be called for every property defined in the materials database.

$Val_{prop,i}(T/p) = f_i(T/p) f_{tot}(T/p) = \sum\limits_i w_i \, f_i(T/p) T/p = f_{tot}^{-1}(Val_{prop,tot})$

The temperature or pressure (e.g. pressure from saturation pressure or different properties) is then calculated in the following steps:

Create tables of value pairs for each compound that is present in the system, i.e. temperature / pressure and respective dependent property value over a certain range of the temperature / pressure.

Combine the compound-lookup tables by mass-weighted summation of the tables.

Read-out of temperature / pressure from the resulting lookup-table at a certain point of the property by interpolation between neighbor value pairs.

The functions in base unit are less time-consuming than the material stream / holdup-function and therefore are implemented for usage during solving process (i.e. function CalculateResiduals), if the composition of the material stream / holdup varies in each iteration.

In Unit library, Heater and HeatExchanger apply thermodynamic calculations.

For material stream and holdup

double CalcTemperatureFromProperty(ECompoundTPProperties Property, double Time, double Value)

Returns temperature of the material stream / holdup for a specific value Value of the property Property at the time point Time. Possible properties are those defined in Material database.

double CalcPressureFromProperty(ECompoundTPProperties Property, double Time, double Value)

Returns pressure of the material stream / holdup for a specific value Value of the property Property at the time point Time. Possible properties are those defined in Material database.

For base unit

double CalcTemperatureFromProperty(ECompoundTPProperties Property,vector<double>& CompoundFractions, double Value)

Returns temperature of a generic system of composition CompoundFractions for a specific value Value of the property Property. Possible properties are those defined in Material database.

double CalcPressureFromProperty(ECompoundTPProperties Property,vector<double>& CompoundFractions, double Value)

Returns pressure of a generic system of composition CompoundFractions for a specific value Value of the property Property. Possible properties are those defined in Material database.

void HeatExchange(CMaterialStream* Stream1, CMaterialStream* Stream2, double Time, double Efficiency);

Performs a heat exchange between material streams Stream1 and Stream2 at specified time point Time with a specified efficiency (0 ≤ Efficiency ≤ 1).

$|\dot Q| = \varepsilon \, |\dot Q_{ideal}| = \varepsilon \, \left | \int_{T_1}^{T_{mix}} \dot m_1\,c_{P,1}(\theta)\,d\theta \right | = \varepsilon \, \left | \int_{T_2}^{T_{mix}} \dot m_2\,c_{P,2}(\theta)\,d\theta \right |$

$\varepsilon$ stands for efficiency and $\theta$ for temperature as an integration variable.