7 Stage MRE

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7 Stage MRE Powered By Docstoc
					September 2006
7-Stage M/RE Impactor Data Reduction Spreadsheet and Supporting Information

Prepared for BGI, Waltham, MA

Patrick T. O'Shaughnessy, PhD
Associate Professor
Department of Occupational and Environmental Health
The University of Iowa
Link to O'Shaughnessy Website

INSTRUCTIONS

This spreadsheet was designed to calculate the mass median aerodynamic diameter (MMAD)
and geometric standard deviation (GSD) associated with a heterogenous aerosol under the
assumption that it exhibits a unimodal log-normal distribution. The method used to determine these
two parameters is based on plotting the cumulative fractions of dust on each stage relative to the
stage cut-diameters on log-probability paper as explained, for example, in the second edition of the
William C. Hinds book, "Aerosol Technology: Properties, Behavior, and Measurement of Airborne
Particles", pages 94-97. A detailed explanation of the spreadsheet development, including an
explanation of the relationship between the slope and intercept of the resulting regression line and the
MMAD and GSD, is given in O'Shaughnessy and Raabe, "A Comparison of Cascade Impactor
Data Reduction Methods", Aerosol Science and Technology 37:187-200 (2003).

There are three worksheets:
           (1) a worksheet to enter raw data and calculate the MMAD and GSD
           (2) a worksheet that develops a graph showing the related histogram of mass-fraction per
           stage relative to the ideal lognormal distribution curve, and
           (3) a worksheet that calculates the fraction of respirable, thoracic, and inhalable dust
           as well as PM1, PM 2.5, and PM10

(1) "Log-Prob" calculation worksheet
           Enter raw data in cells with blue font.
           All calculations needed to determine the MMAD and GSD will be automatically computed.
           The "print area" has been selected to print all values and the graph on a single page.
           Note: the probability scale shown is not generic to Excel and was developed from information
           obtained from a website on Excel "tricks":      Link to Simulated Probability Chart Example
           This development of a probability scale relies on the use of an Add-In for labels mentioned
           in the website. Any adjustments of the plot provided may require that Add-In.
           For users familiar with an inverted version of the log-probability plot, one has been
           provided at the bottom of the worksheet.

(2) "Histogram" worksheet
            This worksheet will be automatically updated when the raw data is entered.
            It provides a histogram of the mass-fraction per stage normalized to stage width relative
            to the ideal log-normal distribution developed from the resulting MMAD and GSD.

(3) "Fractions" worksheet
            This worksheet will be automatically updated when the raw data is entered.
            Additional information is given on that sheet.
Prepared by Patrick O'Shaughnessy for BGI, Waltham, MA.

                                                                       7-STAGE M/RE IMPACTOR DATA REDUCTION
                                                                                                                                                                                     To Create Graph and Determine MMAD and GSD from Interecept and Slope
Trial Name:                                                            Trial 2               Test Date:           08/01/06                                                                     Intercept =     1.035451
                                                                                                                                                                                               Slope =         1.149712
Flow Rate:                                                                     2 lpm
Calibrated:                                                            08/01/06              Sample Time:             180 min                                                        X-Range      Y-Range          Regression

                                                                       Cut Diam.   Initial    Final             Net     Mass/Stage        Cum.         Cum.                                         Log-Dia.        Log Dia      Dia.
STAGE NO.                                                                 mm     Weight, mg Weight, mg       Weight, mg     %             %>           %<                                 Z
     1                                                                        32   150.809     150.951            0.142       2.88            2.88       97.12                            1.899           3.466        3.218     24.990
     2                                                                        16   150.401     150.590            0.189       3.83            6.71       93.29                            1.498           2.773        2.757     15.756
     3                                                                         8   150.127     150.474            0.347       7.04           13.75       86.25                            1.092           2.079        2.291      9.880
     4                                                                         4   150.937     151.898            0.961      19.49           33.24       66.76                            0.433           1.386        1.534      4.635
     5                                                                         2   151.910     153.203            1.293      26.22           59.46       40.54                           -0.239           0.693        0.760      2.139
     6                                                                         1   149.301     150.471            1.170      23.73           83.19       16.81                           -0.962           0.000       -0.070      0.932
     7                                                                       0.5   151.120     151.670            0.550      11.15           94.34        5.66                           -1.584          -0.693       -0.786      0.456
  FILTER                                                                            18.259      18.538            0.279       5.66          100.00
                                                                                                   Sum             4.93 mg



                           100
                                                                                                                                                                                     To create Probability Scale
                                                                                                                                                                                     Label      X-point          Y-Point
                                                                                                                                                                                           0.01 -2.326347874               0.1
                                                                                                                                                                                           0.10 -1.281551566               0.1
                                                                                                                                                                                           0.50 -1.39214E-16               0.1
                                                                                                                                                                                           0.90 1.281551566                0.1
                                                    10                                                                                                                                     0.99 2.326347874                0.1
     Diameter, mm




                                                                                                                                                                                     Unlabeled X-point        Y-Point
                                                                                                                                                                                           0.05 -1.644853627          0.1
                                                                                                                                                                                             0.2 -0.841621234         0.1
                                                                                                                                                                                             0.3 -0.524400513         0.1
                                                                                                                                                                                             0.4 -0.253347103         0.1
                                                                   1                                                                                                                         0.6 0.253347103          0.1
                                                                                                                                                                                             0.7 0.524400513          0.1
                                                                                                                                                                                             0.8 0.841621234          0.1
                                                                                                                                                                                           0.95 1.644853627           0.1


                                                                                                                                                                                      -0.90062     0.183895803
                                       0.1
                                                                         0.1           0.1                  0.1                     0.1
                                                                                 Cumulative Probability Less Than Stated Size


                                                                                               MMAD =                 2.82 mm
                                                                                    Geometric Std.Dev. =              3.16

                                                                                         Concentration =            13.70 mg/m3



                                                                       (The same graph inverted)
                                                                                                                                                                                     To create Probability Scale
                                                                                                                                                                                     Label      X-point          Y-Point
                                                                   0.99                                                                                                                    0.01             0.1 -2.32635
                                                                                                                                                                                           0.10             0.1 -1.28155
                    Cumulative Probability Less Than Stated Size




                                                                                                                                                                                           0.50             0.1 -1.4E-16
                                                                                                                                                                                           0.90             0.1 1.281552
                                                                                                                                                                                           0.99             0.1 2.326348
                                                                   0.90
                                                                                                                                                                                     Unlabeled X-point             Y-Point
                                                                                                                                                                                           0.05              0.1    -1.64485
                                                                                                                                                                                             0.2             0.1    -0.84162
                                                                                                                                                                                             0.3             0.1      -0.5244
                                                                   0.50                                                                                                                      0.4             0.1    -0.25335
                                                                                                                                                                                             0.6             0.1    0.253347
                                                                                                                                                                                             0.7             0.1    0.524401
                                                                                                                                                                                             0.8             0.1    0.841621
                                                                                                                                                                                           0.95              0.1    1.644854

                                                                   0.10




                                                                   0.01

                                                                          0.1                      1.0                       10.0            100.0


                                                                                                         Diameter, mm




                                                                                                                                          446b3478-2040-408d-8c5b-a3cc64c922b2.xls
Prepared by Patrick O'Shaughnessy for BGI, Waltham, MA.

                                  Mass        Normalized
Stage        Diameter Log Diam    Fraction    Frequency
                    50 1.69897
         1          32 1.50515      2.87974    0.148578
         2          16 1.20412     3.832894    0.127326
         3           8 0.90309     7.037112    0.233768
         4           4 0.60206     19.48895    0.647409
         5           2 0.30103     26.22186    0.871071
         6           1        0    23.72744    0.788208
         7         0.5 -0.30103    11.15392    0.370525     "Normalized Mass Frequency" can be more formally label
Filter            0.25 -0.60206    5.658082    0.187957

                                                                                                1

                                                                                               0.9
Values for Graph Series
                                                                                               0.8


                                                                   Normalized Mass Frequency
Histogram                         Log-Normal Curve
Cut Diam     Height               Diameter PDF                                                 0.7
      0.25           0                  0.2    0.0567
      0.25    0.187957                  0.4    0.1891                                          0.6
       0.5    0.187957                  0.6    0.3234
       0.5    0.370525                  0.8    0.4388                                          0.5
         1    0.370525                    1    0.5326
                                                                                               0.4
         1    0.788208                  1.2    0.6067
         2    0.788208                  1.4    0.6642
                                                                                               0.3
         2    0.871071                  1.6    0.7080
         4    0.871071                  1.8    0.7407                                          0.2
         4    0.647409                    2    0.7643
         8    0.647409                  2.2    0.7808                                          0.1
         8    0.233768                  2.4    0.7913
        16    0.233768                  2.6    0.7971                                           0
        16    0.127326                  2.8    0.7990                                                0.1
        32    0.127326                    3    0.7978
        32    0.148578                  3.2    0.7941
        50    0.148578                  3.4    0.7883
        50           0                  3.6    0.7810
                                        3.8    0.7723
                                          4    0.7626                                                      Geometric Std.Dev. =
                                        4.2    0.7521
                                        4.4    0.7410
                                        4.6    0.7295
                                        4.8    0.7175
                                          5    0.7054



                              446b3478-2040-408d-8c5b-a3cc64c922b2.xls
       5.2   0.6931
       5.4   0.6807
       5.6   0.6682
       5.8   0.6559
         6   0.6435
       6.2   0.6313
       6.4   0.6192
       6.6   0.6073
       6.8   0.5955
         7   0.5839
       7.2   0.5725
       7.4   0.5613
       7.6   0.5504
       7.8   0.5396
         8   0.5290
       8.2   0.5187
       8.4   0.5086
       8.6   0.4987
       8.8   0.4890
         9   0.4795
       9.2   0.4703
       9.4   0.4612
       9.6   0.4524
       9.8   0.4437
        10   0.4353
      10.2   0.4270
      10.4   0.4190
      10.6   0.4111
      10.8   0.4034
        11   0.3959
      11.2   0.3886
      11.4   0.3814
      11.6   0.3744
      11.8   0.3676
        12   0.3609
      12.2   0.3544
      12.4   0.3480
      12.6   0.3418
      12.8   0.3357
        13   0.3298
      13.2   0.3240
      13.4   0.3183
      13.6   0.3128
      13.8   0.3074
        14   0.3021
      14.2   0.2969



446b3478-2040-408d-8c5b-a3cc64c922b2.xls
      14.4   0.2918
      14.6   0.2869
      14.8   0.2820
        15   0.2773
      15.2   0.2727
      15.4   0.2682
      15.6   0.2637
      15.8   0.2594
        16   0.2552
      16.2   0.2510
      16.4   0.2470
      16.6   0.2430
      16.8   0.2391
        17   0.2353
      17.2   0.2316
      17.4   0.2279
      17.6   0.2243
      17.8   0.2208
        18   0.2174
      18.2   0.2141
      18.4   0.2108
      18.6   0.2076
      18.8   0.2044
        19   0.2013
      19.2   0.1983
      19.4   0.1953
      19.6   0.1924
      19.8   0.1896
        20   0.1868
      20.2   0.1840
      20.4   0.1813
      20.6   0.1787
      20.8   0.1761
        21   0.1736
      21.2   0.1711
      21.4   0.1686
      21.6   0.1662
      21.8   0.1639
        22   0.1616
      22.2   0.1593
      22.4   0.1571
      22.6   0.1549
      22.8   0.1528
        23   0.1507
      23.2   0.1486
      23.4   0.1466



446b3478-2040-408d-8c5b-a3cc64c922b2.xls
      23.6   0.1446
      23.8   0.1426
        24   0.1407
      24.2   0.1388
      24.4   0.1370
      24.6   0.1352
      24.8   0.1334
        25   0.1316
      25.2   0.1299
      25.4   0.1282
      25.6   0.1266
      25.8   0.1249
        26   0.1233
      26.2   0.1217
      26.4   0.1202
      26.6   0.1186
      26.8   0.1171
        27   0.1157
      27.2   0.1142
      27.4   0.1128
      27.6   0.1114
      27.8   0.1100
        28   0.1086
      28.2   0.1073
      28.4   0.1060
      28.6   0.1047
      28.8   0.1034
        29   0.1022
      29.2   0.1009
      29.4   0.0997
      29.6   0.0985
      29.8   0.0973
        30   0.0962
      30.2   0.0950
      30.4   0.0939
      30.6   0.0928
      30.8   0.0917
        31   0.0907
      31.2   0.0896
      31.4   0.0886
      31.6   0.0876
      31.8   0.0866
        32   0.0856
      32.2   0.0846
      32.4   0.0836
      32.6   0.0827



446b3478-2040-408d-8c5b-a3cc64c922b2.xls
      32.8   0.0817
        33   0.0808
      33.2   0.0799
      33.4   0.0790
      33.6   0.0781
      33.8   0.0773
        34   0.0764
      34.2   0.0756
      34.4   0.0748
      34.6   0.0739
      34.8   0.0731
        35   0.0723
      35.2   0.0716
      35.4   0.0708
      35.6   0.0700
      35.8   0.0693
        36   0.0685
      36.2   0.0678
      36.4   0.0671
      36.6   0.0664
      36.8   0.0657
        37   0.0650
      37.2   0.0643
      37.4   0.0636
      37.6   0.0630
      37.8   0.0623
        38   0.0617
      38.2   0.0611
      38.4   0.0604
      38.6   0.0598
      38.8   0.0592
        39   0.0586
      39.2   0.0580
      39.4   0.0574
      39.6   0.0568
      39.8   0.0563
        40   0.0557
      40.2   0.0552
      40.4   0.0546
      40.6   0.0541
      40.8   0.0535
        41   0.0530
      41.2   0.0525
      41.4   0.0520
      41.6   0.0515
      41.8   0.0510



446b3478-2040-408d-8c5b-a3cc64c922b2.xls
        42   0.0505
      42.2   0.0500
      42.4   0.0495
      42.6   0.0490
      42.8   0.0485
        43   0.0481
      43.2   0.0476
      43.4   0.0472
      43.6   0.0467
      43.8   0.0463
        44   0.0458
      44.2   0.0454
      44.4   0.0450
      44.6   0.0446
      44.8   0.0442
        45   0.0437
      45.2   0.0433
      45.4   0.0429
      45.6   0.0425
      45.8   0.0422
        46   0.0418
      46.2   0.0414
      46.4   0.0410
      46.6   0.0406
      46.8   0.0403
        47   0.0399
      47.2   0.0395
      47.4   0.0392
      47.6   0.0388
      47.8   0.0385
        48   0.0382
      48.2   0.0378
      48.4   0.0375
      48.6   0.0371
      48.8   0.0368
        49   0.0365
      49.2   0.0362
      49.4   0.0359
      49.6   0.0355
      49.8   0.0352
        50   0.0349




446b3478-2040-408d-8c5b-a3cc64c922b2.xls
ncy" can be more formally labeled as: dM/dln(d)




                1                         10                      100

                    Cut Diameter, mm


             MMAD =           2.82   mm
 Geometric Std.Dev. =         3.16




                                               446b3478-2040-408d-8c5b-a3cc64c922b2.xls
Prepared by Patrick O'Shaughnessy for BGI, Waltham, MA.

Dust Fractions Relevant to Industrial Hygiene

                          Fraction    Conc.
                                            3
                                      mg/m
             Respirable    0.461       6.31
             Thoracic      0.732      10.03
             Inhalable     0.873      11.96

Dust Fractions Relevant to EPA Regulations/Concerns

                          Fraction    Conc.
                                            3
                                      mg/m
             PM 1          0.184       2.52
             PM 2.5        0.459       6.28
             PM 10         0.865      11.85


NOTES:
Computation of the Respirable, Thoracic, and Inhalable fractions is based on the ACGIH definition for each.
The definitions define an efficiency curve over a range of particle diameters rather than assume a straight cut-off at a
particular diameter. The equations for each were applied to a separate spreadsheet to determine the
collection efficiency for all particles between the cut-diameters of each stage.
To compute a value for the first and last stage, the first stage was assumed to capture up to 100 micrometers and
the last stage was assumed to capture down to 0.01 micrometers.

ACGIH Sampling Curve Fractions/stage  Corresponding Fractionial Mass of Corrected Net Wt
Stage   Inhalable Thoracic Respirable Inhalable Thoracic Respirable

         1       0.525       0.000      0.000         0.099       0.000       0.000
         2       0.632       0.050      0.000         0.219       0.017       0.000
         3       0.754       0.407      0.013         0.724       0.392       0.012
         4       0.855       0.809      0.235         1.106       1.046       0.304
         5       0.921       0.920      0.753         1.078       1.077       0.881
         6       0.959       0.959      0.952         0.527       0.527       0.523
         7       0.979       0.979      0.979         0.273       0.273       0.273
Filter           0.996       0.996      0.996         0.278       0.278       0.278
                                     Sums             4.304       3.610       2.271


Since EPA-related diameters are not defined in relation to a collection curve, the values computed
below simply represent the fraction of the total distribution of particles with diameters less than or
equal to the stated size. In other words, they are equivalent to values that could be interpreted from the
graph in "Log-Prob" and therefore represent devices with "ideal" collection characteristics.


Although both the "Thoracic" and PM10 have the same cut-diameter of 10 micrometers, the nature of the
collection curve defining the thoracic fraction results in a slightly different fraction than when computing that
fraction as a "straight" cut-off diameter as was done for the PM 10 fraction.




                                          446b3478-2040-408d-8c5b-a3cc64c922b2.xls

				
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