An efficient, reliable and easily programmed method for solving systems of equilibrium stage separation devices is described. The method is an extension of an algorithm developed by Ishii and Otto(9) for single columns. It solves all equations simultaneously, takes advantage of the basic tridiagonal matrix form form of the linearized steady state equations and can handle configurations which include distillation columns, absorbers and reboiled absorbers. The solution for a thermally coupled distillation system is presented.



On decrit une methode efficace, fiable et facilement programmee pour la solution de systemes de dispositifs de separation au stade d'equilibre. Ladite methode est une extension d'un algorithme qu'avaient mis au point Ishii et Otto(9) pour des colonnes simples; elle permet de resoudre toutes les equations simultanement, de tirer profit de la forme fondamentale de la matrice tridiagonale des equations de linearisation en regime stable et de pouvoir s'appliquer aux configurations qui comprennent les colonnes de distillation ainsi que les absorbeurs ordinaires et de type bouilleur. On presente la solution dans le cas d'un systeme de distillation avec thermocouple.

Solving multicolumn equilibrium stage operations by total linearization

Prediction of vaporization efficiencies for multicomponent mixtures by use of existing correlations for the vapor and liquid film coefficients

The block-relaxation method, system-tH equations and a direct sequential calculation have been combined to solve the non-linear algebraic equations describing the steady-state behavior of a multi-recycle network of five distillation towers and two reactors. Approximately 2,000 such equations are solved in 30 minutes of IBM 7040 computation time.



The existence of optimum tolerances on individual column calculations and on individual recycle calculations is demonstrated. The application of the block-relaxation method to a network of distillation columns is numerically shown to simultaneously converge the network equations and the individual column equations to the final solution.



On a utilise a la fois la methode d'approximations successives (relaxation) en bloc., des equations du systeme-tH et un calcnl direct de sequence pour resoudre les equations algebriques et non-lineaires ou l'on decrit le comportement, a regime permanent, d'un reseau a recyclage multiple forme de cinq tours a distillation et de deux reacteurs. On a pu ainsi resoudre a peu pres 2,000 equations de ce genre en 30 minutes au moyen d'un calculateur IBM 7040.



On a prouve l'existence de tolerances optimales dans le cas de calculs individuels de colonnes et de recyclage. On a demontre numeriquement que l'application de la methode d'approximations successives a un reseau de colonnes a distillation fait converger simultanement les equations du reseau et celles d'une colonne individuelle vers la solution finale.

The mathematical representation of a light hydrocarbon refining network

On efficient solution of complex systems of interlinked multistage separators

Solution of systems of columns with energy exchange between recycle streams

A convergence method (called the Θ-method) and calculational procedure have been developed which may be applied to any system of distillation units. The procedure makes use of the programs of the individual units without modification. This amounts to the use of the programs of the individual units as building blocks for the construction of the model for the system. Any number of independent feeds to any one of the distillation units may be specified, and any number of sidestreams may be either withdrawn from the system or fed to any other unit of the system.

T. A. Nartker

Papers

Solution of problems involving systems of distillation columns