Back calculation

The insectivorous bird assessment might also require a back calculation seeking a characterization of concentrations that could ensme the doses of insecticide received by the birds are no larger than can be physiologically tolerated. Suppose the toxicologists have collected evidence that doses lethal for the birds occur above 100 pg g day. Suppose also that regulators have concluded from this information that prudent environmental protection will require that all doses received by birds be less 

Output from traditional Monte Carlo assessment (black) compared to p-box 

FIGURE 6.17 Planned constraints on the distribution of dose (left), and limits on the concentration distribution (right) that ensure dose constraints are not violated. 

Application of Uncertainty Analysis to Ecological Risk of Pesticides 

Following is the run stream used to make the calculations described in Section 6.8. Comments are delimited by double slashes. Output is shown in boldface type. Vertical bars around arithmetic operators mean they should be applied under an independence assumption. 

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Values of A and B for the base component are back-calculated for each stage in the outer loop from a suitable iC-value correlation (e.g. the SRK equation, which is also used to compute the iC values of the other components on each of the other stages so that values of Ot) can be computed). The values of A, B, and Ot are passed from the outer loop to the inner loop, where they are used to formulate the phase equihb-ria equation ... 

Minimum Fluidizing Velocity U,nj, the minimum fluidizing velocity, is frequently used in fluid-bed calculations and in quantifying one of the particle properties. This parameter is best measured in small-scale equipment at ambient conditions. The correlation by Wen audYu [A.l.Ch.E.j., 610-612 (1966)] given below can then be used to back calculate d. This gives a particle size that takes into account effects of size distribution and sphericity. The correlation can then be used to estimate U, at process conditions, if U,nj cannot be determined experimentally, use the expression below directly. 

Agitation by a wide spatula may be substituted for hand agitation, but only after it has been determined by feel that the spatula will provide the needed agitation. If this cannot be done, then confirmation of proper agitation must be based on back-calculated feed solids concentrations and/or particle size analyses of the filter cakes. 

The effective surface viscosity is best found by experiment with the system in question, followed by back calculation through Eq. (22-55). From the precursors to Eq. (22-55), such experiments have yielded values of [L, on the order of (dyn-s)/cm for common surfactants in water at room temperature, which agrees with independent measurements [Lemhch, Chem. Eng. ScL, 23, 932 (1968) and Shih and Lem-lich. Am. Inst. Chem. Eng. J., 13, 751 (1967)]. However, the expected high [L, for aqueous solutions of such sldn-forming substances as saponin and albumin was not attained, perhaps because of their non-newtonian surface behavior [Shih and Lemhch, Ind. Eng. Chem. Fun-dam., 10, 254 (1971) andjashnani and Lemlich, y. Colloid Inteiface ScL, 46, 13(1974)]. 

During this preparation stage, analysts will frequently find that there is insufficient quantity or quality of measurements to close the material balance. Analysts should make eveiy effort to measure aU stream flows and compositions for the actual test. They should not rely upon closing material balances by back-calculating missing streams. Tne material balance closure will provide a check on the vahdity of the measurements. This preparatoiy material balance will help to identify additional measurements and schedule the installation of the additional instruments. 

Back-calculated from next unit Back-calculated to close... 

Rigorous calculation results combined with plant data can be used to back calculate column tray efficiencies for... 

MESOREM Jr. Impell Corporation Becky Cropper 300 Tristate Internat l Suite 400 Lincolnshire, IL 60069 (312) 940-2090 Atmospheric release analysis system that includes back calculations of source release rates from field readings, terrain modeling, meteorological conditions modeling of multipoint dose and deposition exposures. Also provides ingestion exposure reports for atmospheric effluent pathways. 

Klimpel, R.R. and Austin, L.G., 1984. The back-calculation of specific rates of breakage from continuous mill data. Powder Technology, 38, 77-91. 

Now back calculate for the clearance that must be added to produce this volumetric efficiency. 

Table 6.2 presents an overview of surface-emissive powers measured in the British Gas tests, as back-calculated from radiometer readings. Peak values of surface-emissive powers were approximately 100 kW/m higher than these average values, but only for a short duration. Other large-scale tests include those conducted to investigate the performance of fire-protection systems for LPG tanks. 

Use Figure 8-144 to aid in the determination. If more plate area is required than is available, back-calculate the necessary maximum hole velocity. Check if this is reasonable (say not over twice the minimum). If so, the diameter is still acceptable or change the hole spacing to allow more or fewer holes to be placed in the given diameter of the tower. Use limiting values previously given on hole spacing. 

Whether for a distillation, absorption, or stripping system the material balance should be established around the top, bottom, and feed sections of the column. Then, using these liquid and vapor rates at actual flowing conditions, determine the flooding and maximum operating points or conditions. Then, using Figures 9-21B, -21E, or -21F, establish pressure drop, or assume a pressure drop and back-calculate a vapor flow rate, and from this a column diam-... 

It is usually more accurate to back-calculate the feed metals trom the equilibrium catalyst data than to analyze the feed regularly, l nickel will be a regular component of the feed, passivators are available. If nickel affects operation and margins, it is often beneficial to use antimony to passivate the nickel. This can be attractive if the nickel on the equilibrium catalyst is greater than 1,000 ppm. 

Although (5 varies with temperature, the quantity [<5, — 5] is insensitive to temperature the solubility parameters used in Eq. (70) were therefore treated as constants. Table III gives some of the solubility parameters used by Chao and Seader. For supercritical components, the solubility parameters were back-calculated from binary-mixture data, as was also done by Shair (P2). 

Results The raw data consisted of peak height ratios of signal internal standard, see data files VALIDl.dat (primary validation m - 0 repeats at every concentration), VALID2.dat (between-day variability), and VALID3. dat (combination of a single-day calibration with several repeats at 35 and 350 [ng/mlj in preparation of placing QC-sample concentration near these values). Fig. 4.29 shows the results of the back-calculation for all three files, for both the lin/lin and the log/log evaluations. Fig. 4.30 shows the pooled data from file VALID2.dat. 

Figure 4.29. Back-calculated results for files VALIDX.dat. The data are presented sequentially from left to right. The ordinate is in % of the nominal concentration. Numbers X = 1,2, and 3 indicate the data file. Each bracket indicates a day s worth of results (sorted by concentration). The log/log format tends to produce positive deviations at low concentrations, while the lin/lin format does the opposite, to the point of suggesting negative concentrations The reason is that the low concentration values are tightly clustered at the left end of the lin/lin depiction whereas the values are evenly spread in the log/log depiction, with commensurate effects on the position of Xmean, the sum Sxx< and the influence each coordinate has on the slope. The calibration design was optimized for the log/log format.

Back-calculation is achieved by equating the individual calibration signal y i) with y, using Eq. (2.19), and calculating 100 X(y )Anominai [%]. The estimated standard deviation on X(y ), Sx, is transformed to a coefficient of variation by calculation of either CV = 100 /Xnominai or CV =... 

Figure 4.30. Back-calculated results for file VALID2.dat. The data from the left half of Fig. 4.29 are superimposed to show that the day-to-day variability most heavily influences the results at the lower concentrations. The lin/lin format is perceived to be best suited to the upper half of the concentration range, and nearly useless below 5 ng/ml. The log/log format is fairly safe to use over a wide concentration range, but a very obvious trend suggests the possibility of improvements (a) nonlinear regression, and (b) elimination of the lowest concentrations. Option (b) was tried, but to no avail While the curvature disappeared, the reduction in n, logf.t) range, and Sxx made for a larger Pres and. thus, larger interpolation errors.

The back-calculated values (also in -coordinates) as absolute and relative values. 

Figure 4.38. Validation data for a RIA kit. (a) The average calibration curve is shown with the LOD and the LOQ if possible, the nearly linear portion is used which offers high sensitivity, (b) Estimate of the attained CVs the CV for the concentrations is tendentially higher than that obtained from QC-sample triplicates because the back transformation adds noise. Compare the CV-vs.-concentration function with the data in Fig. 4.6 (c) Presents the same data as (d), but on a run-by-run basis, (d) The 16 sets of calibration data were used to estimate the concentrations ( back-calculation ) the large variability at 0.1 pg/ml is due to the assumption of LOD =0.1.

Figure 4.39. Variability of back calculated concentrations Concbc- For each concentration range five calibration points were measured, over which a separate regression was run (not shown). Placebo tablets were spiked to the same concentrations and measured in triplicate (short horizontal lines gray trend lines in background). Ten repeat determinations of actual product (vertical bars = Mean + SD) were done. The bold lines pertain to compound A in all concentration ranges, the thin lines to compound B (middle concentration range only).

Table 4.43. Back-Calculated Data from Method Validation Tests... 

The back-calculated results (99.9 0.9%) for both calibration and spiked samples are acceptable. 

Display Calibration Check Table) Numerical results for the above item, including the back-calculated values in [% of nominal] format. 

The back-calculation feature in option (Display Values) gives each measurement as the absolute estimate X y i)) and normalized to the nominal concentration the normalized results should all be around 100%. The symmetrical limits SD are also given. 

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