Classification of the Methods

The rigorous methods can be divided into four basic classes. These are:

• The 2N Newton methods

• The global Newton or simultaneous correction

The BP methods get their name because the stage temperatures are found by directly solving the bubble point equation. The BP methods generally work best for narrow-boiling, ideal or nearly ideal systems; where composition has a greater effect on temperature than the latent heat of vaporization.

The sum-rates (SR) method is suitable for modelling absorbers and strippers with extremely wide-boiling systems, especially those with non-condensables. In these columns, temperatures are the dominant variables and are found by a solution of the stage energy balances. Compositions do not have as great an influence in calculating the temperatures as do heat effects or latent heats of vaporization.

The 2N Newton methods calculate temperatures and total flow rates together but compositions are still calculated in a separate, dependent step. The name 2N Newton means that there are two equations per stage for a total of 2 x N functions and variables per column solved simultaneously by a Newton-Raphson method. The 2N Newton methods have been shown to work well for wide-boiling mixtures including refinery fractionators, absorber-stripper columns and reboiled absorbers.

The first three classes are referred to as equation tearing or decoupling methods because the MESH equations are divided and grouped or partitioned and paired with MESH variables to be solved in a series of steps. The SC methods attempt to solve all of the MESH equations and variables together. Additional classes are:

• Inside-out methods

• Relaxation methods

• Homotopy-continuation methods

• Nonequilibrium models.

The relaxation, inside-out and homotopy-con-tinuation methods are extensions of whole or part of the first four methods in order to expand the range of columns, and to solve difficult systems or columns. The nonequilibrium models are rate-based or transport phenomena-based methods that do away altogether with the ideal stage concept and eliminate any use of efficiencies. They are best suited for columns where a theoretical stage is difficult to define and efficiencies are difficult to predict or apply by any means.

Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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