While there are many methods available for calculating nmlticomponent distillation, their performances leave much to be desired in many instances. In this paper a new technique is presented which has the following advantages:1. Component volatility ranges do not affect the convergence. Absorbers, strippers, and reboiled absorbers can be calculated with the same algorithm used for distillation problems with no modifications.2 . The presence of nonideal solutions is accounted for rigorously and simply with no change in the method.3. Temperature, key component composition or rate, reflux ratio, recovery, or any other function of condenser or reboiler flows can be used as specifications. Murphree plate efficiencies are taken into account inii rigorous manner. The allowable number of feeds and sidestreams isunlimited. No difficulties are caused by negative flows or rounding errors in multifeed problems.6. The method is based on a linearization of the distillation equations so that convergence accelerates as the solution is approached. This is also true of the WangOleson ( 2 3 ) , , and Tiemey-Bruno (26) algorithms. It is not true of methods based upon the Thiele-Geddes method (5, 7, 11, 22) or unsteady state approach (2, 2 0 ) . 7. No difficulties or complications arise from component flows being very small, hence seeding procedures are unnecessary. The primary disadvantage of the new method is its requirement of storage space which necessitates the use of secondary storage media for medium to large size problems, unless a rather large immediate access memory is available. However, recent trends in the computing industry are toward multiprogramming or time-sharing computers, on one hand, and toward small low cost, diskoriented computers, on the other. Time-sharing would allow this distillation program to retrieve its data from secondary storage while another program was being run. Thus no penalty would need be paid for the relatively slow access time of secondary storage. The small computers rely on disk storage for most problems, so that both these schemes tend to reduce the penalty incurred by requiring a large amount of storage. When a large computer is used the penalty is eliminated.The equations which describe continuous, multicomponent distillation are well known (8, 11, 12, ponents where plate 1 is a condenser and plate n is a reboiler. Furthermore, let sidestreams be specified by the ratio of the sidestream to the stream which remains after they are withdrawn. Figure 1 shows a schematic representation of one such plate. Lij, Vij, and Ti are the variables and Li and Vi will represent the total phase flows.We shall assume that the pressure is known and the plate is adiabatic. Let us examine three types of functions which describe the physical processes on plate i.Enthalpy balance:Component material balances:Equilibrium relationships:Qij is derived from the definitions of the vapor phase klurphree plate efficiency. That is yij -yi + 1,jyi+l,j = 0 N and y represent component mole fractions. In terms of our vari...

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A TECHNIQUE for computing complex equilibria is presented which is well adapted for machine computation. I t has no limitations to systems in which few components predominate. Nonideal gases or condensed phases are easily included. I n a test case on a 10-component gaseous system, it computed on the IBM-704.The problem of chemical equilibrium computation is essentially one of finding a minimum of a function of many variables (normally free energy), subject to constraints, by algebraic manipulation, evaluating partial derivatives with respect to new variables, and equating the partial derivatives to zero.There are three variations on the conventional approach of setting derivatives equal to zero and solving simultaneous equations. The oldest is the conventional equilibrium constant method. The equilibrium equation is derived by considering a small amount of reaction (in which the stoichiometric equation embodies the material balance on the elements) and setting dG = 0. I n the complex case, this results in one nonlinear equation per reaction (see Equation 8).A more recent variation (4) uses the method of Lagrange multipliers to combine a free energy equation with the conservation of the elements constraint. This method also makes use of an algebraic simplification of free energy expression which is dependent on ideal gas expression for chemical potential.The last variation is the conventional minimization approach(2). This method also uses a single expression for free energy of the mixture, algebraically incorporating the material balances, and sets the derivatives equal to zero.In both of these methods (2, 4), simultaneous equations to be solved are fewer in number than the chemical equilibria, and therefore simpler to solve.The present method is based on minimizing free energy by the gradient method. This process is greatly simplified by special relationships which hold for chemical equilibrium. We can describe the change in free energy for chemical react5ons by a AG for each reaction. If we proceed forward in those reactions for which AG is negative .) equilibrium composition in 15 seconds and backward in those for which AG is positive, a decreasing free energy is assured. Then evaluate the composition changes that result and start again. When combined, these steps lead to an algebraically very simple procedure. The result is suited to automatic computation. I t does not require ideal gases; can have any number of phases; and can even be modified to allow computation of equilibrium under constraints other than T a n d P, such as H a n d P for adiabatic flame temperatures, and S and P for isentropic expansions. TheoryThe theory leading to computation of the direction of composition change for which AG 5 0 was published previously ( 3 ) . ,An account is given of it here, which -while not simpler-avoids the use of matrix algebra.A table of stoichiometric coefficients is formed in which each column represents a reaction, and each row a component. The entry is the coefficient in the equation, with a minus sign for c...

The method of nonlinear estimation has been used to fit the coefficients in the equation of state to either vapor-pressure data or P-V-T data.

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