Tearing equations

Equation-Tearing Procedures Using the Tridiagonal-Matrix... 

EQUATION-TEARING PROCEDURES USING THE TRIDIAGONAL-MATRIX ALGORITHM... 

Tridiagonal-Matrix Algorithm Both the BP and the SR equation-tearing methods compute hqnid-phase mole fractions in the same way by first developing linear matrix equations in a manner shown by Amundson andPontinen [Jnd. ng. Ch m., 50, 730 (1958)]. Equations (13-69) and (13-68) are combinedto eliminate yjj and yij + i (however, the vector yj stiU remains imphcitly in K j) ... 

A wide variety of iterative solution procedures for solving nonlinear algebraic equations has appeared in the literature. In general, these procedures make use of equation partitioning in conjunction with equation tearing and/or linearization by Newton-Raphson techniques, which are described in detail by Myers and Seider. The equation-tearing method was applied in Section 7.4 for computing an adiabatic flash. 

Early attempts to solve (15-1) to (15-5) or equivalent forms of these equations resulted in the classical stage-by-stage, equation-by-equation cal-culational procedures of Lewis-Matheson in 1932 and Thiele-Geddes in 1933 based on equation tearing for solving simple fractionators with one feed and two... 

The Lewis-Matheson method is also an equation-tearing procedure. It was formulated according to the Case I variable specification in. Table 6.2 to determine stage requirements for specifications of the separation of two key components, a reflux ratio and a feed-stage location criterion. Both outer and inner iterations are required. The outer loop tear variables are the mole fractions or flow rates of nonkey components in the products. The inner loop tear variables are the interstage vapor (or liquid) flow rates. The Lewis-Matheson method was widely used for hand calculations, but it also proved often to be numerically unstable when implemented on a digital computer. 

Equation-tearing methods, 562-594 Equilateral triangular diagram, in extraction, 106,415 Equilibrium, 89 diagrams, 88-121 heterogeneous, 89 homogeneous, 89 liquid-liquid, 146-147, 223-230 ratio, 145... 

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