Balancing errors

Most balancing methods start from the assumption that the balance model (set of balance equations) holds exactly and that the measured values are subject to random errors only, in a range anticipated by the maximum errors of measurement. This is, of course, an idealised situation which can be violated in practice. 

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Numerical analysts call such problems ill-conditioned. Monitoring the size of the mass-balance error check will alert the user to ill-conditioned data here. 

Protein was measured using the crude protein method (25). Analysis of the percentage of protein may be low, leading to mass balance error. 

Fritz, S. J. (1994). A survey of charge-balance errors on published analyses of potable ground and surface waters. Ground Water 32(4), 539-546. 

PERCENT ERROR Percent charge-balance error [100(cations- anions )/(cations + anions )l... 

The derivatives of the material balance errors with respect to vapor flows are evaluated ... 

The energy balance errors are next differentiated with respect to vapor flows. 

Values for these norms are given in Table I at each iteration. At iteration 9 the maximum error in any equilibrium equation is 2 X 10"6, and the maximum energy balance error is 0.09 Btu/unit time. 

T Activity coefficient matrix for the liquid phase the ij element is the activity coefficient for component j in stage i kj Equal to zero when k j equal to 1.0 when k= j A Activity coefficient matrix for vapor phase the ij element is activity coefficient for component j in stage i v Subscript used to indicate iteration number P Euclidean norm of composition errors, Equation 33 a Euclidean norm of energy balance errors, Equation 34... 

The surface absorptivity or cmissivity of cellulose chars cannot be safely assumed to be near unity. Near unity values are found for wavelengths in the mid-infrared, but at the shorter wavelengths characteristic of thermal radiation in combustion environments, the cmissivity may be closer to 0,8. Significant energy balance errors may be made in assuming higher values. 

As no scoring function is perfect and each scoring function has its own strengths and weaknesses, we can combine different scoring functions to balance errors of one single scoring function and improve the probability of... 

Crystal chemistry of erionites should be computed based upon the guidelines of the IMA Zeolite Report of 1997. The reliabilities of the crystal chemistries of these erionites should be evaluated using the balance error formula of = ((A1- -Fe ) —(Na-I-K)-I-2(Ca -F Mg -F Sr -F Ba))/(Na -P K) -P 2(Ca -P Mg -P Sr -P Ba) X 100. The results of chemical analyses of erionite are only considered to be reliable if the balance error (E%) is equal to or less than 10%. 

Ca is the most abundant extra framework cation. Tsi in the range of 0.68-0.79. Erionite-Ca from Shourdo, Georgia Durkee, OR, USA Beach Creek, OR, USA Montresta, Nuoro, Italy British Columbia, Canada Montecchio Maggiore, Italy Jindivick, Australia Phillip Island, Australia and Faedo, Vicenza, Italy passed the balance error and Mg-content test and reclassified as erionite-Ca. 

K makes up 58% of extra framework cation significant Na, Ca, and Mg are also present. Tsi in the range of 0.74—0.79. Erionite-K from Durkee, OR, USA Rome, OR, USA Yaquina Head, OR, USA Reese River, NV, USA Ortenberg Quarry, Germany Rome, OR, USA and selected samples from Cappadocian region of Turkey passed the balance error and Mg-content test and re-classified as erionite-K. 

Some erionite data from the literature did not pass the balance error test or Mg-content test or both. Some data could not be re-classified as single erionite mineral. Italian samples reported from Montecchio were re-calculated as erionite-Ca and erionite-Na, respectively. Two sets of data from Phillip Island, Australia were re-calculated as both erionite-Ca and erionite-Na. Data from Durkee, OR, USA by three different authors were re-calculated and found as erionite-Ca, erionite-Na, erionite-K, respectively. 

Charge Balance Errors Combined with Line Structure... 

The cut-off value for acceptable charge imbalance is empirical and somewhat arbitrary. Freeze and Cherry (1979) reported that analytical laboratories usually consider a charge-balance error of < 5% to be acceptable. However, for dilute solutions such as rain water, the errors are usually higher. 

RMS MASS BALANCE ERRORS 5.797D-14 MAX. ERROR= 7.165D-14 CN ROW NA4... 

RMS MASS BALANCE ERROR 5.797D-14 MAX. RMS EQUILIBRIUM ERROR 4.441D-15 MAX. 

The root mean square mass balance error. 

Maximum mass balance error and the row having this maximum error. 

The solution is considered valid by the program if both the RMS mass balance error and the RMS mass action error are less than 3 x 10 , and the Valid Solution message... 

Errors. Two types of errors are computed by the program the mass balance errors and the mass action errors. 

Root mean square mass balance error Maximum mass balance error Root mean square equilibrium error (mass action)... 

List of first variable for each compartment List of compartment number for each variable Row number of maximum mass balance error Column number of maximum equilibrium error... 

NEMB 1 I Row number of maximum mass balance error... 

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