Inside-Out Algorithm
This method was developed in the 1980's and has the advantage of quick calculation speed. Two loops are considered in the convergence scheme for the column equations: an inner loop in which simple thermodynamic models are used to converge the performance specification equations and the tray heat balances and an outer loop in which the thermodynamic and enthalpy data are updated and the equilibrium balances are converged for each tray. For the inner loop calculations, stripping factors are used (KV/L), ensuring a material balance for all calculations. The Number of Iterations for the Inside-Out method corresponds to the number of outer loop trials. Many applications reach convergence before the default iteration limit of 30 is reached. For applications with non-ideal thermodynamics in which damping is applied the iteration limit may need to be increased. Inside-Out columns in recycle loops should be completely solved for each recycle trial.
Advantages of Inside-Out:
(1) Fast Convergence
(2) Relatively insensitive to quality of Column Initial Estimates
(3) Column Side Columns are solved simultaneously with the main column
(4) Column Reboiler Types may include thermosiphon.
Disadvantages of Inside-Out:
(1) Only one liquid phase is permitted within the column [a free water phase may be decanted at the condenser]
(2) May be difficult to solve for highly non-ideal thermodynamics
(3) Total pumparounds are not allowed.
Note: Ideal Gas Enthalpy correlation data for all components is required for this algorithm.
Enhanced I/O Algorithm
This method extends the capabilities of the default Inside-Out algorithm. It uses a new solution technique which supports the following features:
Total vapor and liquid side draws
Total pumparounds
Free water phase and water decant on any tray
If water is expected on column trays, you may supply an estimate of the amount of free water in the Initial Liquid Rate Profile Window.
The default number of iterations for the Enhanced I/O Algorithm is 30.
Sure Algorithm
This method uses a classic Newton-Raphson solution technique with matrix partitioning. The algorithm in PRO/II has a long history of development for solution of unusual distillation problems and the method may be applied when other methods cannot be applied successfully. The Sure algorithm also provides some unique features, not available with the other algorithms.
The solution method solves all of the column equations, including the performance specifications, simultaneously. This tends to be more time consuming than the two loop concept used by the Inside-Out method. When side columns are present, they are solved as separate columns in recycle with the main column. While a special recycle procedure is used to speed the calculations, this approach is less efficient than the simultaneous solution method used in the Inside-Out column.
The Sure method may be used to solve two liquid phase problems, where one liquid phase may or may not be water. This makes the method useful for solution of non-ideal chemical applications and for hydrocarbon applications in which free water occurs at column trays other than the condenser.
The Sure method often reaches a solution in the 20 iteration limit supplied as the default. For highly non-ideal problems in which compositional averaging is used the iteration limit should be increased. Sure columns in recycle loops typically solve easier when the iteration limit per recycle loop trial is limited to three or four. For these problems the column and the loop are allowed to converge simultaneously.
Advantages of Sure:
(1) Two liquid phases may be considered
(2) A free water phase and water draws are permitted in columns at trays below the condenser
(3) Total pumparounds are permitted.
Disadvantages of Sure:
(1) Slow calculation speed
(2) Column Initial Estimates must be accurate, particularly the flows
(3) Side columns are solved as a recycle problem
ChemDist Algorithm
This method was designed to solve highly non-ideal distillation columns. It uses a modified Naphtali-Sandholm algorithm with a matrix solver developed by SimSci. Liquid activity coefficients and vapor phase fugacities are used directly rather than being converted to equilibrium K-values. Mole fractions undergo a non-linear mapping which improves convergence.
This is generally the best algorithm for three-phase distillation simulations or for two-phase simulations when the Inside-Out or Enhanced I/O algorithm has difficulty converging.
If you designate a VLLE thermodynamic system for part of the column and a VLE system for the rest, PRO/II checks the VLE trays for possible VLLE behavior. If VLLE behavior is detected, the column may be resolved using VLLE system for these trays. See Column Thermodynamic Systems for more information.
Advantages of ChemDist:
(1) Two liquid phases may be considered
(2) Solves highly non-ideal distillation columns
Disadvantages of ChemDist:
(1) Side columns are not supported
(2) Pumparounds are not available
(3) Certain Column Specifications and Variables are not permitted
(4) Only liquid activity thermodynamic systems or advanced equation-of-state methods may be used.
Electrolytic Algorithm
This method was designed to solve non-ideal aqueous electrolytic distillation columns involving ionic species. It uses a Newton-Raphson method to solve the mass balance, vapor/liquid equilibrium and specification equations simultaneously. The K-values and enthalpies are supplied by the Electrolyte thermodynamic systems.
The electrolytic thermodynamic systems only support VLE and so total phase draws are not permitted.
Advantages of Electrolytic:
(1) Rigorously models ionic equilibrium systems
(2) Solves highly non-ideal distillation columns
Disadvantages of Electrolytic:
(1) Side columns are not supported
(2) Pumparounds and hydraulic calculations are not available
(3) Certain Column Specifications and Variables are not permitted.
Liquid-Liquid Algorithm
This method simulates the operation of multi-component liquid-liquid extraction columns using a modification of the Naphtali-Sandholm block tridiagonal matrix method. The liquid-liquid extraction column is treated as a column made up of theoretical trays. Two insoluble liquid phases are contacted on the trays with the components to be extracted being selectively transferred from the heavy liquid phase to the light phase.
The thermodynamic system selected for the liquid-liquid extraction column must be a liquid activity method which is capable of predicting liquid/liquid equilibrium.
Complete technical details may be found in topics under Distillation and Liquid-liquid Extraction Columns in the PRO/II Reference Manual.
RATEFRAC® Routine
The rate based RATEFRAC® algorithm is the only distillation algorithm in PRO/II that rigorously models non-equilibrium separations. PRO/II uses the term "stage" to differentiate rate-based calculations from "theoretical trays" in equilibrium models.
Advantages of RATEFRAC®
1. Rate based distillation rigorously calculates the actual mass transfer on the stage, avoiding the need for component efficiencies.
2. The non-equilibrium stage model in RATEFRAC®uses fundamental heat and mass transfer to model a distillation tray or a segment of packing in a packed tower. Different mass transfer correlations are available for trays, structured packing and random packing.
3. Boiling Pot Reactor: A RATEFRAC® reactive distillation column configured with one tray can simulate a boiling pot reactor. To accomplish this, specify the bottoms product flow rate to be zero (0.0). In all cases, the boiling pot reactor is modeled on the bottom tray of the column. Note that there is no specific keyword or GUI option for a boiling pot reactor. Also, RATEFRAC does not support the non-volatile catalyst option. Boiling pot reactions must have reaction products that are more volatile than the reactants.
4. User-Added Utility Calculations: Being rate based rather than equilibrium based, RATEFRAC® is the only column algorithm that supports user-written utility subroutines to calculate interfacial area between the vapor and bulk liquid phases, binary mass transfer between phases, and heat transfer between phases. For more information about implementing these procedures, refer to chapter 4 of the User-Added Subroutine User Guide.
Disadvantages: Chemdist Features Not Available in rate-based RATEFRAC® calculations:
1. L1/L2 Basis Reactions: RATEFRAC® does not support two liquid phase calculations; therefore L1 and L2 bases are not valid for reactions.
2. Mixed Phase Reactions: RATEFRAC® requires that all participating reactants and products belong to the same phase. Mixed phase reactions are not supported.
3. Non-Volatile Catalyst: RATEFRAC® does not support the non-volatile catalyst option (typically used elsewhere when modelling a boiling pot rector).
4. Non-Condensable: RATEFRAC® does not allow designating specific components as non-condensable.
5. User Added Subroutines: User added reaction subroutines (written in FORTRAN) are not supported in the current release. However, In-line kinetic procedures are supported and may be used for user defined kinetics.
