Solution criteria

Nontrace isothermal systems give the adsorption effect (i.e., significant change in fluid velocity because of loss or gain of solute). Criteria for the existence of simple waves, contact discontinmties, and shocks are changed somewhat [Peterson and Helfferich, J. Phy.s. Chem., 69, 1283 (1965) LeVan et al., AIChE J., 34, 996 (1988) Frey, AJChE J., 38, 1649(1992)]. 

Errors in the MESH equations of Sec. 4.1.2 should be small, including the stage energy total material and component balances and summation equation should be small. The physical solution criteria above should take precedence over any mathematical criteria, such as having Newton-Raphson functions approach zero (Sec. 4.2.6). 

Convergence is achieved when the 0 s are very nearly unity and all other solution criteria (see Sec. 4.2.3) have been met, If not solved, return to the component balances of step 2. 

In addition to the solution criteria in Sec. 4.2.3, the Newton-Raphson method requires an additional check on convergence, This check, termed the norm or the square root of the sum. of the squares, tests that all of the functions are driven nearly to zero ... 

The norm of the independent functions must be very small at the solution (see Sec. 4.2.6 for criteria). If it is not small or other solution criteria (Sec. 4.2.3) have not been met, return to step 2. 

Besides the usual solution criteria, there is one additional criterion for the relaxation method. The maximum difference between a composition and temperature on any stage calculated in the last trial and the previous should be very small, i.e.,... 

With Emvo = 0.1, solve the Naphtali-Sandholm method for the column, The solution criteria for intermediate valueB of MVy (0.1,... 

The circumstances above explain why there is little evidence of pressure solution even in Cambrian, Ordovician and other sandstones buried to 5 000 m and more. The large amount of authigenic quartz viewed in cathodoluminescence microscopy, despite little evidence of pressure solution criteria, suggests that a more appropriate mechanism for silica authigenesis in sandstones needs to be identified. 

Solution criteria. With any rigorous method it is imperative to set criteria to determine when a solution is reached. Each rigorous method has its own unique criteria, but they all must conform to some phs i-cal criteria. Section 4.1,1 states that at solution, overall mass, component, and energy balances are achieved. There are other criteria a method should meet. If there are specifications such as product flow... 

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