ASTM E2776-20

Standard Guide for Correlation of Results of Solid Particle Size Measurement Instruments

SIGNIFICANCE AND USE
4.1 It is useful to be able to obtain particle size measurement results of a user specified product from multiple instruments and to be able to correlate the results of the measurements. This capability can be advantageous in expanding the use of different technologies to make a measurement or simply to correlate results between instruments of the same technology. An example might be comparing in-process particle size measurements to final inspection particle size measurements.  
4.2 The viability of this guide will need to be tested on a case-by-case basis as various products may present measurement challenges for some instruments and not all results from all instruments may be able to be correlated to all other results from all other instruments. In addition, positive results should be confirmed and improved with continued data comparisons over time using process measurements from the instruments selected.
SCOPE
1.1 This guide describes one methodology to correlate solid particle analysis results between solid particle analysis instruments for user specified products of user specified particle sizes and distributions in order to expand the capability of particle measurement throughout the manufacturing process and provide better control and efficiency. The guide is not limited to instrument type or product type.  
1.2 Warning—Not all instruments may correlate to all other instruments for various user specified products and size ranges. Instruments may measure different particle features, and they may also measure the same particle features differently and thus correlating the results of any two may be possible for some products but not possible for others. It is also the case that certain materials can be altered by the instruments measuring them which would eliminate them from consideration under this guide if the instrument’s results are determined based on measurements made after the instrument has altered the user specified product.  
1.3 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 30-Sep-2020
• ICS: 19.120 - Particle size analysis. Sieving
• Technical Committee: E29 - Particle and Spray Characterization
• Drafting Committee: E29.02 - Non-Sieving Methods

Overview

ASTM E2776-20 is the Standard Guide for Correlation of Results of Solid Particle Size Measurement Instruments, developed by ASTM International. This guide provides a methodology to correlate results obtained from different solid particle size analysis instruments measuring user-specified products with defined particle size distributions. The primary goal is to enable comparison of results across various types or models of instruments, enhancing measurement capability and improving process control and efficiency within manufacturing environments.

Particle size distribution is a critical quality parameter in sectors such as pharmaceuticals, chemicals, mining, and materials processing. Since a variety of instrument technologies exist-each with potential differences in measurement principles and data output-ASTM E2776-20 seeks to promote reliable, cross-platform comparison and data integrity in solid particle analysis.

Key Topics

• Correlation Methodology: Outlines a systematic procedure for users to correlate particle size distribution results obtained from two or more instruments, including:

  • Selection and preparation of representative product samples
  • Determination of sample size and statistical significance
  • Adjustment of measurement bin boundaries to match across instruments
  • Iterative testing and validation of results

• Instrument Variability: Recognizes that correlation may not be possible between all instrument pairs, due to differences in:

  • Measurement technologies used (e.g., sieving, imaging, laser diffraction)
  • Product characteristics
  • The potential for certain instruments to alter sample properties during measurement

• Reporting Requirements: Details what information to include in correlation reports, such as instrument descriptions, software versions, and clear statements regarding correlated results.

• Quality Assurance: Recommends ongoing data comparison and periodic verification to maintain accuracy and repeatability in correlated measurements.

• Limitations and Responsibilities: Reminds users to address safety, health, and regulatory compliance, and to use SI units exclusively.

Applications

ASTM E2776-20 is valuable across industries where particle size measurement is essential for quality control, research, or regulatory compliance. Typical applications include:

• Manufacturing Process Control: By correlating in-process and final inspection data from different instruments, organizations gain better control over product specifications and consistency.
• Cross-Technology Comparison: Enables effective data comparison between traditional sieving and advanced instruments, such as optical imaging or laser analyzers.
• Multi-Site Coordination: Facilitates standardized particle size reporting across different facilities or laboratories that may use distinct measurement systems.
• Supplier and Customer Communication: Supports reliable exchange of particle size data even when different analytical methods are used, reducing disputes and streamlining supply chains.
• Product Development and R&D: Enhances the ability to compare experimental data obtained from various particle sizing methodologies, accelerating material innovation.

Related Standards

To ensure robust particle size measurement and reporting, organizations may also reference:

• ASTM E2651 - Standard Guide for Powder Flow Testing for Additive Manufacturing
• ASTM E1617 - Standard Guide for Reporting Sieve Analysis Results
• ASTM D4464 - Standard Practice for Determining Particle Size Distribution of Metal Powders and Related Compounds
• ISO 13320 - Particle Size Analysis - Laser Diffraction Methods
• ISO 9276 Series - Representation of Results of Particle Size Analysis

Implementing ASTM E2776-20 as part of a comprehensive quality or materials testing program helps mitigate the risk of inconsistency across measurement techniques and supports global best practices in solid particle size analysis. For full compliance, always use the up-to-date ASTM standard and review related industry standards as applicable.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E2776 − 20
Standard Guide for
Correlation of Results of Solid Particle Size Measurement
Instruments
This standard is issued under the fixed designation E2776; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope* 2. Terminology
1.1 This guide describes one methodology to correlate solid 2.1 Definitions of Terms Specific to This Standard:
particle analysis results between solid particle analysis instru- 2.1.1 bin, n—a user specified division of the overall particle
mentsforuserspecifiedproductsofuserspecifiedparticlesizes
size range of a user specified product.
and distributions in order to expand the capability of particle
2.1.2 correlation, n—mathematical equation(s) relating one
measurement throughout the manufacturing process and pro-
set of numerical values to another.
vide better control and efficiency. The guide is not limited to
2.1.3 particle analysis instrument, n—any instrument of any
instrument type or product type.
type that can produce a particle size distribution measurement
1.2 Warning—Not all instruments may correlate to all
of a product. There is no restriction on technology or method-
other instruments for various user specified products and size
ology used by the instrument to measure particles nor is there
ranges. Instruments may measure different particle features,
any restriction of particle characteristics used to report results
and they may also measure the same particle features differ-
of the measurement.
ently and thus correlating the results of any two may be
2.1.4 user specified product, n—indicates a product manu-
possible for some products but not possible for others. It is also
factured by the user to a specified size distribution, usually
the case that certain materials can be altered by the instruments
indicated by common sieve screen sizes.
measuring them which would eliminate them from consider-
ation under this guide if the instrument’s results are determined
3. Summary of Guide
based on measurements made after the instrument has altered
the user specified product. 3.1 This guide describes a method which can be used to
correlate results between instruments which measure particle
1.3 The values stated in SI units are to be regarded as
size, and distribution, of materials by the same or different
standard. No other units of measurement are included in this
parameters and principles.
standard.
3.2 The primary interest is the correlation of particle size
1.4 This standard does not purport to address all of the
measurements of user specified products.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
3.3 This guide can be used for any two particle measuring
priate safety, health, and environmental practices and deter-
instruments which output a user specified distribution and have
mine the applicability of regulatory limitations prior to use.
the capacity to shift bin boundaries within the software.
1.5 This international standard was developed in accor-
Therefore, a set of sieves cannot correlate to another
dance with internationally recognized principles on standard-
instrument, but another instrument may correlate to the set of
ization established in the Decision on Principles for the
sieves. Ideally, the bin boundaries for the correlating instru-
Development of International Standards, Guides and Recom-
ment would match the bin boundaries of the primary
mendations issued by the World Trade Organization Technical
instrument, or if correlating to sieves, match the range of each
Barriers to Trade (TBT) Committee.
corresponding sieve, but if they do not, the method described
in this guide could be used to adjust the individual bin
boundaries used by the correlating instrument to make the
volume percent detected for each bin closely match the percent
retained by each corresponding bin of the primary instrument
This guide is under the jurisdiction of ASTM Committee E29 on Particle and
or set of sieves.
Spray Characterization and is the direct responsibility of Subcommittee E29.02 on
Non-Sieving Methods.
3.4 The guide is valid for any two instruments as long as it
Current edition approved Oct. 1, 2020. Published October 2020. Originally
can be demonstrated that the correlation results are useful to
approved in 2018. Last previous edition approved in 2018 as E2776 – 18. DOI:
10.1520/E2776-20. the user.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2776 − 20
4. Significance and Use 5.6 Calculate the variation and average repeatability of the
correlating instrument based on these results. Ideally, the
4.1 Itisusefultobeabletoobtainparticlesizemeasurement
repeatability would be better than5%inthe highly populated
results of a user specified product from multiple instruments
bins. The user will have to make a judgment on the applica-
andtobeabletocorrelatetheresultsofthemeasurements.This
bilityofanycorrelationbasedontheaccuracyandrepeatability
capability can be advantageous in expanding the use of
of the correlating instrument involved and the precision needed
different technologies to make a measurement or simply to
to control the process.
correlate results between instruments of the same technology.
An example might be comparing in-process particle size
5.7 If the results are acceptable, then verify the set up by
measurements to final inspection particle size measurements.
running the remaining twenty samples. If adjustments are
required, make them and then re verify. Determine the final
4.2 The viability of this guide will need to be tested on a
accuracy and repeatability of the correlation and determine if it
case-by-case basis as various products may present measure-
is adequate for measuring the process.
ment challenges for some instruments and not all results from
all instruments may be able to be correlated to all other results
5.8 Once the correlation is confirmed, the software file of
from all other instruments. In addition, positive results should
the correlating instrument must be saved as a unique file
be confirmed and improved with continued data comparisons
containing the fixed settings and correlation for the particular
over time using process measurements from the instruments
user specified product tested. If either the primary or correlat-
selected.
ing instrument are altered in a way that might affect measure-
ment results, this entire procedure must be repeated.
5. Procedure
NOTE 1—Depending on instrument type and features, this procedure
5.9 It is recommended that the correlation be tested near the
might not exactly match the steps required to create a correlation on a
specification boundaries.An example is given in Appendix X3.
particular instrument. The steps referenced herein are meant to guide the
user toward creating a correlation by following similar logic appropriate
to the instrument selected. 6. Report
5.1 The first step is for the user to select a particular
6.1 The particle distribution produced by the correlating
manufactured product which has a defined particle size range
instrument should be reported using the gradations identified
and distribution already determined by the user’s sieves or
for the user specified product.
other instrument.
NOTE 3—Changing the bin boundaries will not change the name of the
NOTE 2—Ideally, distributions will be reported in discreet gradations;
bin. For example, a 325 mesh bin might have its boundary shifted from 44
however, this guide can also be used where the determination of the
µm to 35 µm, but it is still identified as the 325 mesh bin.
distribution is a continuous curve.
6.2 Report the correlating instrument model and software
5.2 The procedure requires the gathering of twenty-one
version as well as the file name and version containing the
representative samples of the user specified product which will
correlation. Include a statement indicating the instrument is
be used to determine a correlation which can be used for future
reportingresultscorrelatedtoanotherinstrumentinaccordance
measurements.
with this guide. Indicate the primary instrument and reference
5.3 The sample size (mass) can be determined by assessing
this guide. It may also be informative to include the correlation
the statistical particle count for the largest bin size that will
results in a format similar to the tables presented in Section
yield a particular confidence level. The example in Annex A1
X2.1. An example report format follows:
illustrates the exercise in a straight forward manner.
Correlation Report
5.4 Using the gradations indicated in the user’s product
Primary Instrument: (include identifying information; model #, serial number
specification, determine the particle size distribution of each
etc.{)
sample using the primary instrument of measure. Confirm that Correlating Instrument: (include identifying information; model, serial number
etc.{)
the instrument is in good calibration in accordance with the
Sample: (include sample product name, lot, date run and any other identifying
manufacturer’s instructions or a standard procedure appropri-
codes as appropriate)
ate to the industry. Results: (report size distribution of sample in tabular or graphical form)
5.5 Run one sample through the correlating instrument three
7. Keywords
times and create a correlation by shifting the bin boundaries so
the result closely matches the primary instrument result. 7.1 bin; correlation; distribution; particle size
E2776 − 20
ANNEX
(Mandatory Information)
A1. DETERMINATION OF SAMPLE SIZE
A1.1 As indicated in 5.3, it is important to select a sample A1.3.2 Calculate the number of particles required in the
size that will yield a high enough number of particles for largest bin. Assume all particles at the median bin size, in this
statistical significance. A straight forward way to do this is case 90 microns.
detailed in this annex by means of an example.
1⁄2
Sn 5 1⁄~n !
n 5 number of particles
A1.2 Assumptions
n 5 1 ⁄ 0.05
~ !
(A1.1)
A1.2.1 Particle range: 1 µm – 100 µm.
n 5 400 particles required
A1.2.2 Five gradations (bins) as follows with 20 % by mass
A1.3.3 With the number of particles now calculated for the
in each: pan, 20 µm, 40 µm, 60 µm, and 80 µm. Fewest number
topbin,aminimumsamplemasscanbeprojectedfortheentire
of particles will reside in the 80-µm bin, so using that as the
sample by converting the 20 % bin mass to 100 %.Assume the
limiting factor of the analysis, compute the number, and then
product density is 1 g/cm .
mass, of sample required.
24 3 3
Sample Mass 5 400 3 100 ⁄ 20 3 Pi ⁄ 6 3 90 3 10 cm
~ ! @~ ! ~ ! #
A1.3 Method
31g⁄cm 5 0.00076g (A1.2)
A1.3.1 Select a standard error (Sn) allowable. The standard
error is the measured standard deviation of a sample. For this One must still ensure that the correlating instrument actually
example, 5 % will be used. measures the minimum number of particles (n).
APPENDIXES
(Nonmandatory Information)
X1. SAMPLE CORRELATION
X1.1 Sample Description (7) 70 USS, and
(8) PAN.
X1.1.1 The sample used in this illustration of the correlation
is silica frac sand. Correlation is between a sieve stack and an X1.2.2 Product distribution is defined as follows:
imaging system. (1) 90 % passing 30 screen and retained above 50 screen,
(2) No more than 0.1 % on 20 screen, and
X1.2 User Specified Distribution
(3) No more than1%on70 screen.
X1.2.1 Sieves that make up the distribution of this sand are
X1.3 Analysis of Sample 1
as follows:
(1) 20 USS, X1.3.1 Sample 1 is taken from production inventory at a
(2) 30 USS, sand manufacturing facility. Table X1.1 shows the percentage
(3) 35 USS, in each bin as sieved (on the left) and the raw correlating
(4) 40 USS, instrument results after three runs (on the right) and the
(5) 45 USS, correlated values in bold type in Column 4 of Table X1.1.
(6) 50 USS, Correlation is within 1.5 % for each bin.
TABLE X1.1 Sample 1
Sample 1 Sample 1
Instrument Results
Sieve Results Uncalibrated
Bin Grams % Recal Run Run 1 Run 2 Run 3 Std Dev r (%)
20 USS 0.05 0.05 0 20 USS 1.09 0.74 0.78 0.19 42.94
30 USS 2.67 2.72 2.43 30 USS 21.03 19.48 17.49 1.77 17.97
35 USS 16.69 17.03 16.07 35 USS 39.98 39.51 38.00 1.03 5.17
40 USS 51.10 52.13 51.25 40 USS 30.41 31.65 33.75 1.69 10.37
45 USS 22.70 23.16 24.64 45 USS 6.79 7.56 8.75 0.99 25.20
50 USS 4.21 4.29 4.92 50 USS 0.51 0.76 0.88 0.19 50.88
70 USS 0.56 0.57 0.61 70 USS 0.16 0.25 0.28 0.06 52.65
Pan 0.05 0.05 0.06 Pan 0.03 0.05 0.06 0.02 68.87
Total 98.03 100.00
E2776 − 20
TABLE X1.2 Imaging – Sieve Comparison of a 30/50 Frac Sand Sample
Sieve Imaging Correlated Shifted Bin Shifted Bin
US Sieve Size
% Retained % Retained % Retained Low End High End
20 0 0.1 0.08 850 850+
30 4.1 7.8 4.2 634.9 –850
50 95 91.4 95 310.9 –634.9
70 0.8 0.6 0.7 224.4 –310.9
Pan 0.2 0.1 0.02 0 –224.4
TABLE X1.3 Sample 2
selected to match and the instrument boundaries corresponding
Correlating to that sieve were adjusted to include a revised number of
Bin Mass (g) %
Instrument
particles to better match the percent retained on the corre-
20 USS 0.05 0.05 0
sponding sieve. The remaining gradations were then adjusted
30 USS 2.26 2.39 3.81
to match the sieves they correspond to. In this particular case,
35 USS 20.46 21.60 18.82
40 USS 49.69 52.46 51.1 the boundary changes were made by the software; however,
45 USS 19.28 20.35 22.3
manual changes could also have been made. Changes may
50 USS 2.78 2.93 3.73
need to occur on an iterative basis.
70 USS 0.20 0.21 0
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E2776 − 18 E2776 − 20
Standard Guide for
Correlation of Results of Solid Particle Size Measurement
Instruments
This standard is issued under the fixed designation E2776; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope Scope*
1.1 This guide describes one methodology to correlate solid particle analysis results between solid particle analysis instruments
for user specified products of user specified particle sizes and distributions in order to expand the capability of particle
measurement throughout the manufacturing process and provide better control and efficiency. The guide is not limited to
instrument type or product type.
1.2 Warning—All Not all instruments may not correlate to all other instruments for various user specified products and size
ranges. Instruments may measure different particle features, and they may also measure the same particle features differently and
thus correlating the results of any two may be possible for some products but not possible for others. It is also the case that certain
materials can be altered by the instruments measuring them which would eliminate them from consideration under this guide if
the instrument’s results are determined based on measurements made after the instrument has altered the user specified product.
1.3 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
This guide is under the jurisdiction of ASTM Committee E29 on Particle and Spray Characterization and is the direct responsibility of Subcommittee E29.02 on
Non-Sieving Methods.
Current edition approved April 1, 2018Oct. 1, 2020. Published May 2018October 2020. Originally approved in 2018. Last previous edition approved in 2018 as E2776
– 18. DOI: 10.1520/E2776-18.10.1520/E2776-20.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2776 − 20
2. Terminology
2.1 Definitions of Terms Specific to This Standard:
2.1.1 bin, n—a user specified division of the overall particle size range of a user specified product.
2.1.2 correlation, n—mathematical equation(s) relating one set of numerical values to another.
2.1.3 particle analysis instrument, n—any instrument of any type that can produce a particle size distribution measurement of a
product. There is no restriction on technology or methodology used by the instrument to measure particles nor is there any
restriction of particle characteristics used to report results of the measurement.
2.1.4 user specified product, n—indicates a product manufactured by the user to a specified size distribution, usually indicated by
common sieve screen sizes.
3. Summary of Guide
3.1 This guide describes a method which can be used to correlate results between instruments which measure particle size, and
distribution, of materials by the same or different parameters and principles.
3.2 The primary interest is the correlation of particle size measurements of user specified products.
3.3 This guide can be used for any two particle measuring instruments which output a user specified distribution and have the
capacity to shift bin boundaries within the software. Therefore, a set of sieves cannot correlate to another instrument, but another
instrument may correlate to the set of sieves. Ideally, the bin boundaries for the correlating instrument would match the bin
boundaries of the primary instrument, or if correlating to sieves, match the range of each corresponding sieve, but if they do not,
the method described in this documentguide could be used to adjust the individual bin boundaries used by the correlating
instrument to make the volume percent detected for each bin closely match the percent retained by each corresponding bin of the
primary instrument or set of sieves.
3.4 The guide is valid for any two instruments as long as it can be demonstrated that the correlation results are useful to the user.
4. Significance and Use
4.1 It is useful to be able to obtain particle size measurement results of a user specified product from multiple instruments and
to be able to correlate the results of the measurements. This capability can be advantageous in expanding the use of different
technologies to make a measurement or simply to correlate results between instruments of the same technology. An example might
be comparing in-process particle size measurements to final inspection particle size measurements.
4.2 The viability of this guide will need to be tested on a case-by-case basis as various products may present measurement
challenges for some instruments and not all results from all instruments may be able to be correlated to all other results from all
other instruments. In addition, positive results should be confirmed and improved with continued data comparisons over time using
process measurements from the instruments selected.
5. Procedure
NOTE 1—Depending on instrument type and features, this procedure might not exactly match the steps required to create a correlation on a particular
instrument. The steps referenced herein are meant to guide the user toward creating a correlation by following similar logic appropriate to the instrument
selected.
5.1 The first step is for the user to select a particular manufactured product which has a defined particle size range and distribution
already determined by the user’s sieves or other instrument.
NOTE 2—Ideally, distributions will be reported in discrete gradations howeverdiscreet gradations; however, this guide can also be used where the
determination of the distribution is a continuous curve.
5.2 The procedure requires the gathering of twenty-one representative samples of the user specified product which will be used
to determine a correlation which can be used for future measurements.
E2776 − 20
5.3 The sample size (mass) can be determined by assessing the statistical particle count for the largest bin size that will yield a
particular confidence level. The example in Annex A1 illustrates the exercise in a straight forward manner.
5.4 Using the gradations indicated in the user’s product specification, determine the particle size distribution of each sample using
the primary instrument of measure. Confirm that the instrument is in good calibration in accordance with the manufacturer’s
instructions or a standard procedure appropriate to the industry.
5.5 Run one sample through the correlating instrument three times and create a correlation by shifting the bin boundaries so the
result closely matches the primary instrument result.
5.6 Calculate the variation and average repeatability of the correlating instrument based on these results. Ideally, the repeatability
would be better than 5 % in the highly populated bins. The user will have to make a judgment on the applicability of any correlation
based on the accuracy and repeatability of the correlating instrument involved and the precision needed to control the process.
5.7 If the results are acceptable, then verify the set up by running the remaining twenty samples. If adjustments are required, make
them and then re verify. Determine the final accuracy and repeatability of the correlation and determine if it is adequate for
measuring the process.
5.8 Once the correlation is confirmed, the software file of the correlating instrument must be saved as a unique file containing the
fixed settings and correlation for the particular user specified product tested. If either the primary or correlating instrument are
altered in a way that might affect measurement results, this entire procedure must be repeated.
5.9 It is recommended that the correlation be tested near the specification boundaries. An example is given in Appendix X3.
6. Report
6.1 The particle distribution produced by the correlating instrument should be reported using the gradations identified for the user
specified product.
NOTE 3—Changing the bin boundaries will not change the name of the bin. For example, a 325 mesh bin might have its boundary shifted from 44 μm
to 35 μm, but it is still identified as the 325 mesh bin.
6.2 Report the correlating instrument model and software version as well as the file name and version containing the correlation.
Include a statement indicating the instrument is reporting results correlated to another instrument per in accordance with this guide.
Indicate the primary instrument and reference this document.guide. It may also be informative to include the correlation results
in a format similar to the tables presented in Section X2.1. An example report format follows:
Correlation Report
Primary Instrument: (include identifying information; model #, serial number etc.{)
Correlating Instrument: (include identifying information; model, serial number etc.{)
Sample: (include sample product name, lot, date run and any other identifying codes as appropriate)
Results: (report size distribution of sample in tabular or graphical form)
7. Keywords
7.1 bin; correlation; distribution; particle size
E2776 − 20
ANNEX
(Mandatory Information)
A1. DETERMINATION OF SAMPLE SIZE
A1.1 As indicated in 5.3, it is important to select a sample size that will yield a high enough number of particles for statistical
significance. A straight forward way to do this is detailed in this annex by means of an example.
A1.2 Assumptions
A1.2.1 Particle range: 1 μm – 100 μm.
A1.2.2 Five gradations (bins) as follows with 20 % by mass in each: pan, 20 μm, 40 μm, 60 μm, and 80 μm. Fewest number of
particles will reside in the 80-μm bin, so using that as the limiting factor of the analysis, compute the number, and then mass, of
sample required.
A1.3 Method
A1.3.1 Select a standard error (Sn) allowable. The standard error is the measured standard deviation of a sample. For this example,
5 % will be used.
A1.3.2 Calculate the number of particles required in the largest bin. Assume all particles at the median bin size, in this case 90
microns.
1⁄2
Sn 5 1⁄ n
~ !
n 5 number of particles
n 5 1 ⁄ 0.05
~ ! (A1.1)
n 5 400 particles required
A1.3.3 With the number of particles now calculated for the top bin, a minimum sample mass can be projected for the entire sample
by converting the 20 % bin mass to 100 %. Assume the product density is 1 g/cm .
24 3 3 3
Sample Mass 5 400 3 100 ⁄ 20 3 Pi ⁄ 6 3 90 3 10 cm 31g⁄cm 5 0.00076 g (A1.2)
~ ! @~ ! ~ ! #
One must still ensure that the correlating instrument actually measures the minimum number of particles (n).
E2776 − 20
APPENDIXES
(Nonmandatory Information)
X1. SAMPLE CORRELATION
X1.1 Sample Description
X1.1.1 The sample used in this illustration of the correlation is silica frac sand. Correlation is between a sieve stack and an imaging
system.
X1.2 User Specified Distribution
X1.2.1 Sieves that makeup make up the distribution of this sand are as follows:
(1) 20 USS,
(2) 30 USS,
(3) 35 USS,
(4) 40 USS,
(5) 45 USS,
(6) 50 USS,
(7) 70 USS, and
(8) PAN.
X1.2.2 Product distribution is defined as follows:
(1) 90 % passing 30 screen and retained above 50 screen,
(2) No more than 0.1 % on 20 screen, and
(3) No more than 1 % on 70 screen.
X1.3 Analysis of Sample 1
X1.3.1 Sample 1 is taken from production inventory at a sand manufacturing facility. Table X1.1 shows the percentage in each
bin as sieved (on the left) and the raw correlating instrument results after three runs (on the right) and the correlated values in bold
type in Column 4 of Table X1.1. Correlation is within 1.5 % for each bin.
TABLE X1.1 Sample 1
Sample 1 Sample 1
Instrument Results
Sieve Results Uncalibrated
Bin Grams % Recal Run Run 1 Run 2 Run 3 Std Dev r (%)
20 USS 0.05 0.05 0 20 USS 1.09 0.74 0.78 0.19 42.94
30 USS 2.67 2.72 2.43 30 USS 21.03 19.48 17.49 1.77 17.97
35 USS 16.69 17.03 16.07 35 USS 39.98 39.51 38.00 1.03 5.17
40 USS 51.10 52.13 51.25 40 USS 30.41 31.65 33.75 1.69 10.37
45 USS 22.70 23.16 24.64 45 USS 6.79 7.56 8.75 0.99 25.20
50 USS 4.21 4.29 4.92 50 USS 0.51 0.76 0.88 0.19 50.88
70 USS 0.56 0.57 0.61 70 USS 0.16 0.25 0.28 0.06 52.65
Pan 0.05 0.05 0.06 Pan 0.03 0.05 0.06 0.02 68.87
Total 98.03 100.00
E2776 − 20
TABLE X1.2 Imaging – Sieve Comparison of a 30/50 Frac Sand Sample
Sieve Imaging Correlated Shifted Bin Shifted Bin
US Sieve Size
% Retained % Retained % Retained Low End High End
20 0 0.1 0.08 850 850+
30 4.1 7.8 4.2 634.9 –850
50 95 91.4 95 310.9 –634.9
70 0.8 0.6 0.7 224.4 –310.9
Pan 0.2 0.1 0.02 0 –224.4
TABLE X1.2X1.3 Sample 2
Correlating
Bin Mass (g) %
Instrument
20 USS 0.05 0.05 0
30 USS 2.26 2.39 3.81
35 USS 20.46 21.60 18.82
40 USS 49.69 52.46 51.1
45 USS 19.28 20.35 22.3
50 USS 2.78 2.93 3.73
70 USS 0.20 0.21 0.22
Pan 0.00 0.00 0.01
Total 94.72 100.00
X1.3.2 In this example, the boundaries of the bins used by the correlating instrument were adjusted so that the total percent mass
of each bin matched closely with the corresponding gradation of the primary instrument, in this case a sieve. The requirements
stated in Sec
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