Procedure for Use of Electronic Digital Computers in Calculating Flash Vaporization Hydrocarbon Equilibrium

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Abstract The effectiveness of digital computing machines in making technicalcalculations depends on how well the work is arranged to utilize the capabilityof the machines. This note presents a particularly useful way of calculatinghydrocarbon vapor-liquid equilibrium in the flash vaporization (orcondensation) system. The method is well suited to sequence-controlledcomputing equipment. It is not limited to equilibrium calculations and may beused for solution of most implicit equations in one variable. Introduction There is increasing interest in the use of electronic digital computers inresearch and engineering calculations. This is a fortunate and inevitable trendin view of both the increasingly extensive numerical work which is becoming aroutine part of many daily production operations and growing demand for theoverwhelming amounts of calculations required by newly developed numericalmethods for solving heretofore unsolved problems. Machines are in many ways ideally suited to the task but of necessitypresent certain difficulties for a particular problem to be solved must oftenbe formulated quite differently from the way it would be arranged for manualsolution. This is done in order to take advantage of the inherent speed andprecision of electronic computers and at the same time to limit the need fornumber storage to the capacity of the machine. Therefore, this note issubmitted to present a general and quite powerful method of finding solutionsof the frequently encountered implicit equation: (Equation 1) where the root, x0, is to be found for a given set of y1… yn. Theprocedure is well suited for use with computing machines, for it usuallyrequires but little storage or programming beyond that necessary to evaluateF. Hydrocarbon Equilibrium The method is described in terms of the problem it was designed to solve, i.e., the calculation of hydrocarbon vapor-liquid equilibrium in flashvaporization. Given the composition of a hydrocarbon mixture and appropriatevalues of the equilibrium ratios K, to find the phase ratio and compositions ina closed system: let zi be the mol fraction of the i-th component in themixture. T.N. 136