Tridiagonal matrix method

In the inner-loop calculation sequence, component flow rates are computed from the MESH equations by the tridiagonal matrix method. The resulting bottoms-product flow rate deviates somewhat from the specified value of 50 lb mol/h. However, by modifying the component stripping factors with a base stripping factor, S, in (13-109) of 1,1863, the error in the bottoms flow rate is reduced to 0,73 percent. 

Calculating the component flow rates. The tridiagonal matrix method introduced by Wang and Henke (24), is a fast and accurate technique for calculating the component and total flow rates. This method for calculating the component flow rates is used in most of the following rigorous methods. 

Based on the most recent set of temperatures and total flow rates, calculate the component vapor rates using the tridiagonal matrix method. Find the component liquid rates by l j = Ay i>y,... 

In the SR method, temperatures are the dominant variables and are found by a Newton-Raphson 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 component flow rates are found by the tridiagonal matrix method. These are summed to get the total rates, hence the name sum rates. 

Set initial temperatures and total vapor and liquid rates for each stage. Calculate initial component vapor rates using the tridiagonal matrix method and find the component liquid rates by applying the absorption factor, Zy = i y. 

Russell organizes the tridiagonal matrix method to calculate the component liquid rates instead of the vapor rates (as in Sec. 4.2.3) but either can be used. The component vapor rates are found by = Sy l . The total flow rates are found by summing the component flow rates ... 

EXAMPLE 13.1 COMPONENT FLOW RATES BY THE TRIDIAGONAL MATRIX METHOD... 

Calculate the component liquid rates by the tridiagonal matrix method. Component vapor rates are found by the component (not the base) stripping factors, Uy =... 

Example 13.1 Component flow rates by the tridiagonal matrix method... 

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