Equation oriented techniques

Hence, factorization methods can only be applied to solve particular cases of data reconciliation when energy balances are considered. Other equation-oriented techniques, such as PLADAT (Sanchez et al., 1992), perform better in tackling the more general problem. 

Starting with a compound s molecular structure, the T, P, and are estimated first, using the three group contribution techniques indicated above. These values are then used in an equation-oriented technique to yield the final estimate for P. ... 

We need to employ an estimation procedure for and the associated independent physical properties, such as those described in Section I.B [see Eqs. (2) and (3a-c)], in order to determine each candidate molecule s vapor pressure at 273 K. Starting with a compound s molecular structure, and P are first estimated using the three group-contribution techniques [Eqs. (3a), (3b), and (3c), respectively]. These values are then used in an equation-oriented technique to yield the final estimate for P [Eq. (2)1. 

P (Fi Fj Fj) - JobacW Pc Factor - Equation Oriented Technique P () - Joback Pc - Group Contribution Technique... 

The Riedel method is an example of an equation oriented estimation technique for predicting the enthalpy of vaporization at the solvent s normal boding point (Reid et al., 1987) ... 

Interval values for these fundamental properties can be used in equation-oriented estimation techniques. The Watson relation (Watson, 1943)... 

Incorporating these equation-oriented estimation techniques into a new estimation procedure for yields the following correlation, proposed by... 

Physical property estimation procedures are at the heart of the design procedures. The group-contribution section provides facilities for entering group contribution and equation oriented correlations. Models in the form of LISP code are entered for both types of estimation techniques. Additionally, groups and their contributions are specified for group contribution techniques. 

Two extremes are encountered in flowsheeting software. At one extreme, the entire set of equations (and inequalities) representing the process is employed. This representation is known as the equation-oriented method of flowsheeting. The equations can be solved in a sequential fashion analogous to the modular representation described below or simultaneously by Newton s method, Broyden s method, or by employing sparse matrix techniques to reduce the extent of matrix manipulations. Refer to the review by Evans and Chapter 5. ... 

Equation-oriented approaches ate based on sets of equations that are written for the units in a particular flowsheet. Unlike the sequential-modular systems, which often contain the necessary information for a variety of process units, equation-oriented synthesizers require the practitioner to develop the model equations. These are solved through iterative techniques with standard numerical methods. 

The classical scheme for dichroism measurements implies measuring absorbances (optical densities) for light electric vector parallel and perpendicular to the orientation of director of a planarly oriented nematic or smectic sample. This approach requires high quality polarizers and planarly oriented samples. The alternative technique [50, 53] utilizes a comparison of the absorbance in the isotropic phase (Dj) with that of a homeotropically oriented smectic phase (Dh). In this case, the apparent order parameter for each vibrational oscillator of interest S (related to a certain molecular fragment) may be calculated as S = l-(Dh/Di) (l/f), where / is the thermal correction factor. The angles of orientation of vibrational oscillators (0) with respect to the normal to the smectic layers may be determined according to the equation... 

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