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D Total vapor distillate rate.

Dj Term of simple vapor enthalpy model in the inside-out methods, de fined by Eq. (4.92).

d Total liquid distillate rate.

dt Component distillate rate, component i.

Ej Energy balance as a function for a stage in Sees. 4.2.7 to 4.2.9.

Ej Term of simple liquid enthalpy model in the inside-out methods, defined by Eq. (4.93).

Emvy Murphree efficiency, component i, stage j, defined by Eq. (4.20).

Vaporization efficiency, component i, stage j, defined by Eq. (4.23).

E*j Net energy gain by a phase in a nonequilibrium method, stagey,

e Perturbed value for xk in a derivative of a Newton-Raphson solu tion, Sec. 4.2.6.

e, Energy flux for energy transfer between two phases, stage Sec. 4.2.13.

etJ Equilibrium equation in a global Newton method, Sec. 4.2.9.

Ff Total feed rate, stage f.

Fj Term of simple liquid enthalpy model in the inside-out methods, defined by Eq. (4.93).

F, Vector of independent functions of stage j, for a Newton-Raphson solution in a Naphtali-Sandholm or nonequilibrium method.

F(x) Vector representing the difficult, desired solution in a homotopy method, Sec. 4.2.12.

F Vector of total feed rates to a column in the total material balances.

ft Rate of component in the feed to a column, fk Independent function of a Newton-Raphson solution, Sec. 4.2.6.

fijL Fugacity of the liquid, K- value, component i, stage j.

fij v Fugacity of the vapor, A'-value, component i, stagej.

f, Vector of component feed rates to a column, component i, Sec. 4.2.4.

f* Vector of values for the independent functions in a Newton-

Gix) Vector of function values for the easier solution in a homotopy method, Sec. 4.2.12.

kB Molar enthalpy of bottoms product.

Hd Molar enthalpy of distillate product, liquid or vapor phase.

Hw Molar enthalpy of side product, liquid or vapor phase.

Hj Molar enthalpy of vapor phase, stage./.

H°, Molar ideal gas enthalpy of vapor phase, stage./.

Hjr Enthalpy of a feed, encompassing all phases, feed F.

Ht Jacobian at each homotopy step t, Sec. 4.2.12.

Hj. Jacobian of the known solution in a homotopy method, Sec. 4.2.12.

H(x^) Jacobian of derivatives of the homotopy matrix, Sec. 4.2.12.

hJ Molar enthalpy of liquid phase, stage j.

h°j Molar ideal has enthalpy of liquid phase, stagey.

Jfc Jacobian of partial derivatives in Newton-Raphson method, trial k,

Kij Equilibrium constant, if-value, component i, stagey.

Kbj A'-value for base component of the Kb method and the simple K-

value model of the inside-out methods, stagey, Sec. 4.2.10.

Lj Internal total liquid rate, stagey.

L0 Lean oil feed rate to the top stage of an absorber.

L1 External total reflux rate; internal total liquid rate, stage 1.

Lfc Lower triangular matrix of LU factorization, trial k, Sec. 4.2.6.

ilF Component liquid rate in the feed, component i.

ly Internal component liquid rate, component /, stagey.

Mj Total material balance as a function for a stage in Sec. 4.2.9.

m,j Element of middle diagonal in tridiagonal matrix, component t, stage y, Eq. (4.33).

m^ Component balance in a global Newton method, Sec. 4.2.9.

N Last or total number of stages.

N0 Molar flux for mass transfer between two phases, component i, stagey, Sec. 4.2.13.

Nj Net material gain by a bulk phase in a nonequilibrium method, stagey, Sec. 4.2,13.

normA Square root of the sum of the squares of the functions, trial k, Sec. 4.2.6.

n Number of independent equations and variables in a Newton-

Raphson method, Sec. 4.2.6.

Pj Stage pressure, stagey.

p: Correction factor for stage compositions in the 6 method, compo nent i, defined by Eq. (4.49).

Pij Variable of the Boston inside-out method, defined by Eq. (4.95).

(?c Condenser duty.

Qr Reboiler duty.

Qs Duty of intercondenser or interreboiler of some stage.

Q, Duty to a bulk phase in a nonequilibrium method, stagey, Sec.

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