N Newtonraphson Method For Single Columns

The development of this application of the Newton-Raphson method is presented first for an absorber (or stripper)—see Fig. 4-1. Then the method is applied to conventional and complex distillation columns.

Absorber and strippers may be classified as complex columns because they possess two feeds and because they possess neither an overhead condenser nor a reboiler. The sketch of the absorber in Fig. 4-1 depicts an historic application of absorbers in the natural gas industry. From a light gas stream such as natural gas that contains primarily methane plus small quantities of, say, ethane through n-pentane, the desired quantities of the components heavier than methane may be removed by contacting the natural gas stream with a heavy oil stream (say n-octane or heavier) in a countercurrent, multiple-stage column such as the one shown in Fig. 4-1. Since absorption is a heat-liberating process, the lean oil is customarily introduced at a temperature below the average temperature at which the column is expected to operate. The flow rate of the lean oil is denoted by L0, and the lean oil enters at the top of the column as implied by Fig. 4-1. The rich gas (which is sometimes called the wet gas) enters at the bottom of the

V2 V2i

Ljw l2

Figure 4-1 Absorber and identifying symbols.

Figure 4-1 Absorber and identifying symbols.

column at a temperature equal to or above its dew-point temperature at the column pressure but generally below the average operating temperature of the column. The total-flow rate of the rich gas is denoted by VN+l. The absorber oil plus the material that it has absorbed leave at the bottom of the column; this stream is called the rich oil. The treated gas leaving the top of the column is called the lean gas (or the stripped gas).

Strippers are used to remove relatively light gases from a heavy oil stream by contacting it with a relatively light gas stream such as steam. Figure 4-1 is also used to depict a typical stripper.

Formulation of the 2N Newton-Raphson Method for an Absorber (or Stripper) with Any Number of Equilibrium Stages

In the following formulation of the Newton-Raphson equations, the independent variables are taken to be the N-stage temperatures {7}} and the N-ratios of the total-flow rates {Lj/Vj}. When the gas and liquid phases form ideal solutions, the procedure described is an exact application of the Newton-Raphson method.

The absorber (or stripper) shown in Fig. 4-1 is described by the N(2c + 3) independent equations. When these equations are stated in terms of component and total-flow rates instead of mole fractions, one obtains

Equilibrium relationships

Component-material balances Energy balances

Equilibrium relationships

Was this article helpful?

0 0

Post a comment