Equilibrium Calculation
The Equilibrium Calculation functionality is used to compute the resulting equilibrium conditions for a mixture of a set of species and phases.
Equilibrium calculations are often used for processes with vapor-liquid equilibrium (VLE), so-called flash calculations. A typical process that requires flash calculations is a distillation process, where a multiphase feed stream is separated into a vapor and a liquid product, and where the concentrations of the species in each phase are required. Equilibrium calculations involve combining the VLE-equations with material balances for the chemical species, and in some cases with an energy balance. Flash calculations are typically used to obtain estimates of:
The last three examples are often considered more difficult, since they require energy balances and relations for computing enthalpy and entropy. The Liquid & Gas Properties Module can handle all of the above cases using the equilibrium calculation functionality. Phase envelopes, bubble point, and dew point can be calculated for any number of species.
Right-click the relevant Thermodynamic System node (see Figure 6-8), Predefined System node, or the relevant External Thermodynamic System node, and select Equilibrium Calculation to start the Equilibrium Calculation Wizard.
The Equilibrium Calculation Wizard consists of the following steps:
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The Equilibrium Calculation settings include three types of equilibrium functions.
Select species
Select one or more of the species available in the thermodynamic system and use the Add Selected button () to add them to the Selected species table. Click the Next button () to proceed to the next step in the wizard.
Equilibrium Specifications
Use the Amount base unit list to use either kg or mol as base unit.
Select two Equilibrium conditions that define the current equilibrium, for example a given pressure and a temperature. These equilibrium conditions are used as arguments in the equilibrium functions, in addition to the composition (overall fractions of species).
The available equilibrium conditions are: Temperature, Pressure, Phase fraction, Energy (or Internal energy of formation), Enthalpy (or Enthalpy of formation), Specific volume, Density and Entropy (or Entropy of formation). For chemical reactions, it is recommended to use Enthalpy of formation, Entropy of formation, or Internal energy of formation, since they account for heat of reactions.
Figure 6-21: Equilibrium Calculation Wizard; Equilibrium Specifications.
Selecting Phase fraction as one of the equilibrium conditions activates the Solution type input field. This can be used to indicate the direction of the desired solution, which is of great use especially near critical points. The options Undefined, Normal, or Retrograde define different directions for the search of the solution to the equilibrium equations. Using Normal means that the derivative of the vapor phase fraction with respect to temperature (at constant pressure and composition) is kept positive and the derivative of the vapor phase fraction with respect to pressure (at constant temperature and composition) is kept negative. Using Retrograde means that the opposite sign of the previous mentioned derivatives are enforced.
For a single species, the critical point is the highest pressure and temperature at which two phases (liquid and vapor) are distinguishable. However, for some multispecies systems, the critical point is a point between the dew point and the bubble point. In this case, the critical point does not represent the maximum pressure or the maximum temperature of vapor-liquid coexistence. This phenomenon is known as retrograde condensation. This means that under isothermal conditions, when the pressure decreases, some of the vapor condenses into liquid instead of expanding or vaporizing. An example of such system is formation of liquid hydrocarbons in a gas reservoir as the pressure decreases below the dew point pressure. In this case, setting Solution type to Normal or Retrograde may not be sufficient to distinguish between the two solutions.
Note that the Solution type setting is only available for a built-in thermodynamic systems. For external thermodynamic systems, the corresponding functionality needs to be supplied by the thermodynamic software provider. For instance, the COCO/TEA provider does not support the Normal or Retrograde options. In those cases, the Solution type should be Undefined.
Click the Next button () to proceed to the next step.
Equilibrium Function Overview
In this step, you can review all the functions including units and arguments. Click the Finish button () to exit the wizard and add functions at equilibrium state to the current thermodynamic system.
The Equilibrium Calculation Node
When creating an Equilibrium Calculation, the resulting functions are collected under the Mixture node. You can create new functions from an existing Mixture node. Right-click it and select Equilibrium Calculation to start the Equilibrium Calculation Wizard (see Figure 6-20).
Settings
Selecting an Equilibrium Calculation node displays the settings including the property functions, see Figure 6-22.
Plot Parameters:
Can be used to evaluate and plot the equilibrium function for a range of argument values. First specify which of the included functions to plot. Then apply a Lower limit and Upper limit for each argument and click the Plot button ().
Figure 6-22: Settings window; Equilibrium calculation.