U7p Total side product withdrawal rate, stage p.

WLj Total liquid side product rate used in the withdrawal factors of the Russell method, Sec. 4.2.10.

WVJ Total vapor side product rate used in the withdrawal factors of the Russell method, Sec. 4.2.10.

u'i Weighting factor in Sec. 4.2.10, component i.

Rate of component i in the side product of stage j.

XDl Composition of top product, covering all phases, of component i.

XlF Composition in feed, covering all phases, component i, feed F.

X, Vector of independent variables of stage j, for a Newton-Raphson solution in a Naphtali-Sandholm or nonequilibrium method, Sec. 4.2.9 and 4.2.13.

xv Liquid composition, component i, stage j.

xh Independent variable in a Newton-Raphson solution, Sec. 4.2.5

only.

x* Vector of independent variables in Newton-Raphson method, trial k, Sec. 4.2.6.

x Vector of independent variables in a homotopy solution, Sec. 4.2.12.

y^j Vapor composition, component i, stagey'.

y*tj Equilibrium composition of the vapor for the Murphree vaporiza tion efficiency, component i, stage j, defined by Eq. (4.20).

4.4.2 Greek letters a^ Relative volatility, used in the Kb method and in the simple K-value model of the inside-out methods, component t, stage j.

A/i^ Liquid-phase enthalpy departure, stagey".

i\HVj Vapor-phase enthalpy departure, stage j.

ATk Temperature span used to generate constants of Kb method, Eq. (4.54).

A/ Time step in the relaxation methods of Sec. 4.2.11.

A** Change in the independent variable .x* to move it toward solution in a Newton-Raphson method, trial k, Sec. 4.2.6.

Axj Vector of the changes in the independent variables in a Newton-Raphson method, trial k, Sec. 4.2.6.

■y*y Simple activity coefficient used in the inside-out methods component i, stage j, Sec, 4.2.10.

6 Theta convergence promoter as defined by Eq. (4.46).

0j Independent variable used as a multiplier on the ratio of total liquid rate to total vapor rate in the 2N Newton-Raphson method, defined by Eq. (4.76).

4.4.3 Subscripts actual Rigorously calculated if-value or enthalpy for any component, in the inside-out or homotopy methods, Sees. 4.2.10 and 4.2.12.

ca Compositions or flows calculated by component material balances in the theta method and 2N Newton-Raphson method, Sees. 4.2.5 and 4.2.8.

co Corrected composition or flows by theta in the theta method and

2JV Newton-Raphson method, Sees. 4.2.5 and 4.2.8.

F Column feed stream.

f Feed stage.

k Trial number of the solution in any method.

min Minimum value limit on a MESH variable.

max |
Maximum value limit on a MESH variable. |

n |
Number of independent functions and variables in a Newton- |

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