Bulk Density

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ESTIMATION OF BULK DENSITY FOR MINERAL RESOURCE REPORTING
*G. J. Arseneau
SRK Consulting (Canada) Inc.
1066-2200 West Hastings Street
Vancouver, Canada
(*Corresponding author:[email protected])

ESTIMATION OF BULK DENSITY FOR MINERAL RESOURCE REPORTING
ABSTRACT
Mineral resource statements are reported as tonnage and grades. While great care is placed on
generating a reliable estimation of grade, the determination of bulk density for resource estimation is often
overlooked. Often mineral resource statements are prepared using a simple average value of bulk density.
While a simple average estimate of bulk density can be appropriate for some deposit types, an over
simplistic estimation of bulk density can result in serious errors in tonnage estimates and consequently to
an over or under estimation of metal content. The construction of a reliable bulk density model requires an
adequate bulk density database in order to develop a good understanding of the variability of bulk density
with grade and geology. A reliable bulk density database is also essential in determining the appropriate
modeling technique to minimize the errors in mineral resource statements caused by incorrect bulk density
determinations. This paper summarizes bulk density measuring techniques and draws on examples from
various deposit types examining the basic principles of bulk density modeling and domain construction for
each deposit type. Examples are presented of simple bulk density domains and more complex grade
variable bulk density domains with a discussion of best approaches for minimizing errors in density
estimation.
KEYWORDS
Bulk density, Specific gravity, Estimation, Mineral resources
INTRODUCTION
Mineral resources are the main assets of mining companies and inaccuracies in reported mineral
resources can have serious financial impacts on the company. The preparation of a mineral resource and
mineral reserves is a team effort that incorporates a number of different facets (Dominy et al., 2004). The
final result of the estimation process is reported in a mineral resource or mineral reserve statement
summarising the average grade and tonnage inside a volume that has the reasonable prospect of economic
extraction. The average grade of the mineralisation is generally determined by geostatistical estimation
and most companies and Qualified Persons (QP) have been concentrating on assuring that grade estimates
are prepared with the most reliable data available with the implementation of rigorous quality assurance
and quality control (QA/QC) protocols. The tonnage of the resource is calculated by multiplying the
estimated volume by the bulk density of the rock hosting the mineralization, yet often little effort seems to
have been placed on assuring the same level of accuracy to bulk density determination. Inaccuracies in
bulk density estimation can lead to errors in reconciliation, or worse, to vanishing mineral reserves (Dias et
al., 2012; Northern Miner, 1988).
The author’s survey of fifty publicly filed technical reports on the System for Electronic
Document Analysis and Retrieval (SEDAR) indicates that while most companies collect bulk density data,
the majority calculate their resource tonnages by averaging all the bulk density measurements. Very few
try to analyse the information collected to attempt to generate a more robust estimate of bulk density.
In order to prepare a reliable resource estimate, proper care must be given to accurately model and
estimate bulk density. Constructing an accurate bulk density model is dependent on the understanding of
the inhomogeneity of the material to be modelled. The estimation parameters and procedures vary greatly
depending on the material to be estimated.
DEFENITIONS
Density (ρ) is the proportion or amount of mass (m) per unit of volume (v) as expressed in
equation 1. Dry bulk density is the proportion of mass including cavities and pore spaces within the
measured volume. In situ bulk density includes naturally occurring water contained within the volume as

well as void. The difference between in situ bulk density and dry bulk density is a measure of contained
moisture within the rock volume. The International System unit of density is gram per cubic centimetres
(g/cm3) or tonnes per cubic metres (t/m3) for most mining projects and resource statements.
ρ = m/v

(1)

Specific gravity (SG) is the ratio of the density of a substance compared to the density of fresh
water at 4°C. Because SG is a ratio, it has no unit of measure. It is common practice in the mining industry
to use the terms SG and density interchangeably; however the two can be very significantly different in
rocks with large voids or porosity (Lipton, 2000).
MEASURING BULK DENSITY
Bulk density can be measured in the field during the geological logging or in the laboratory and at
costs that are usually a fraction of the assaying cost. Several methods of measuring bulk density are
available depending on the properties of the material to be measured (Lipton, 2001). The most commonly
used field method of measuring bulk density follows Archimedes’ Principle of water displacement. The
method works well for competent material and involves weighing the sample in air (ma) and then weighing
the sample suspended in water (mw) (Figure 1). Bulk density is then calculated using the formula
expressed in equation 2.

Figure 1 – Determination of bulk density by water displacement method
ρ = ma/(ma-mw)

(2)

Samples that are friable or clay rich may disintegrate in water and should be coated with wax prior
to water immersion. Ideally, the sample selected for bulk density measurement should be the same size as
the sample collected for assay. This is often not practical because of the difficulty of accurately weighing
one or two metre of drill core. For this reason, the bulk density sample is usually a subset of the assay
sample length, 10 or 15 centimetre of core is normally used. Selecting a subsample of the assay length can
introduce errors if the bulk density of the assay interval is not constant due to high variability of metal
content over the interval. In these circumstances, several bulk density measurements should be taken over
the assay interval so that a more representative density value can be estimated. A commonly used
alternative to field measurement of bulk density is the determination of density by pycnometer. The
pycnometer measures density on pulverized material. The method can be accurate and reliable if the rock
contains very low porosity but the method should be avoided for highly porous material.
DENSITY DOMAINING
Bulk density is a geologically controlled variable and should be modelled as any other geological
variable. Ideally, bulk density data should be treated with the same level of statistical analysis as the assay

data. The level of complexity of the bulk density model is dependent on the variability of bulk density
within the deposit volume to be estimated.
Simple Density Domains
For most vein hosted gold deposits, where only a small concentration of metal is present and no
correlation exists between grade and density, creating a bulk density domain can be as simple as averaging
the density data within the mineralised domain (Figure 2).

Figure 2 – Bulk density example of quartz vein hosted gold deposit
Although no correlation exists between grade and bulk density, the density data exhibit a
significant scatter between 2.75 and 3.0 t/m3. The scatter may be indicative of sampling errors or of a true
local variation in bulk density. Using the average of all data to estimate the bulk density of the resource in
this situation is probably acceptable. The average of all measurements is 2.88 t/m3 the inter quartile range
of the data is 0.15 t/m3 representing a 5% possible error. If the scatter is simply due to sampling error,
additional careful sampling would undoubtedly reduce the scatter and apparent error. d with additional
density data. While a simple average of bulk density measurements may be satisfactory to estimate the
density of the mineralised quartz vein, the same may not necessarily apply to the wall rock hosting the
mineralisation. Weathering or alteration associated with mineralisation often decreases the rock bulk
density and increasing porosity. This may result in high variability in host rock bulk density that may
require complex modelling techniques.
Variable Density Domains
For metal deposits where a relationship exists between bulk density and metal grades such as iron
or uranium deposits, the relationship between bulk density and grade can normally be expressed as a
function of the grade and a density value can be derived from the estimated grade (Figure 3). The average
of all density measurements for the iron deposit in Figure 3 is 2.20 t/m3 and the inter quartile range is 0.26
t/m3. Using a simple average value for the iron deposit will result in an incorrect local density assignment
and inaccurate resource statement. A better approach is to calculate the bulk density of each sample based
on the regression function of measured bulk density against grade. Note that the relationship between
grade and density is approximately linear for the grades and density measurements collected for this
deposit. For data sets with large variation in grades and bulk density, this relationship is not normally a

straight line because density is expressed in terms of volume whereas grades are expressed in weight
percent (Figure 4) (Lipton 2000).

Figure 3 – Bulk density example of iron oxide deposit

Figure 4 – Bulk density example of base metal deposit
Complex Density Domains
For deposits with high variability in grades and density such as massive sulphide or uranium
deposits, estimating bulk density from a regression function is often incorrect and will usually result in
under estimation of bulk density and resource tonnage (Figure 5). Note that the high variability of bulk
density over very small grade ranges in Figure 5 can be attributed to the small size of the sample selected
for bulk density and of the inhomogeneity of the grade distribution over the assay sample length. This
problem can easily be resolved by collecting more than one bulk density measurement per assay interval
and averaging all the bulk density measurements over the assay interval.

Figure 5 – Bulk density example of uranium deposit
For deposits with high variability in grades and density, weighting the assays with density as well
as length or volume should be considered (Sinclair and Blackwell, 2002). Consider the following simple
example, four samples of equal volume with grades and corresponding density as outlined in Table 1. The
total contained metal of the combined volume or parent block (PB) is the sum of the contained metal in the
four sub samples, 1.53 tons. The volume weighted grade (gPB) of the parent block calculated by averaging
the grades of the four sub blocks of equal volume is 8% and the average density (ρPB) of the parent block is
3.5. Estimating the contained metal of the parent block without considering density weighting will result
in an incorrect metal content of 1.12 tons instead of 1.53 tons (Equation 3). Weighting the grade by
density as well as volume returns an average block grade of 10.93% (Equation 4) and returns the correct
metal contents for the parent block (Equation 5).

Sub block
1
2
3
4
Parent Block

Table 1 – Bulk density weighting example
Metal grade (%)
Bulk density (t/m3)
Contained metal (ton)
4
2.5
0.1
2
2.5
0.05
6
3.0
0.18
20
6.0
1.2
8
3.5
1.53
(gPB * ρPB)*4 = 1.12 t

(3)

Ʃ (g1*ρ1+g2*ρ2+g3*ρ3+g4*ρ4)/ Ʃ ρ = 10.93%

(4)

(10.93*3.5)*4 = 1.53 t

(5)

The impact of weighting by density as well as lengths will vary depending on the variance of the
data used to estimate the block grades. Deposits high in lead, uranium or tungsten will return more reliable
tonnage estimates if density weighting is incorporated as part of the resource estimation.
DISCUSSION
The modelling of bulk density for resource estimation can be complex and intricate and each
deposit type needs to be carefully evaluated to determine the most appropriate methodology to best model
bulk density. The author’s survey of fifty publically filed technical reports on SEDAR, twenty-nine
precious metal, ten base metal, seven porphyry and four rare metal deposits seems to indicate that bulk
density is only marginally considered when preparing resource estimates (Table 2). The reports were
selected at random and included six pre-feasibility (PFS) reports, six preliminary economic assessment
(PEA) reports and thirty-eight mineral resource reports. Nine of the reports examined failed to mention
bulk density or to indicate how bulk density was assigned to the resource estimate, three of these were PFS
and one was a PEA. Of the reports that included a discussion of bulk density sampling, most used the
water displacement method for calculating bulk density. On average, bulk density was measured for less
than 20% of the assay data. Twenty-nine reports used a simple average value to estimate bulk density, one
was a PFS and three were PEA level reports. Of the 10 base metal deposits examined four used a simple
average and six estimated the bulk density by geostatistical method with two reports including bulk density
weighting in the estimation methodology. All reports indicated that multiple geological domains were
present yet most used the same bulk density value to estimate the resource tonnage for all domains
ignoring that multiple geological domains may indicate multiple bulk density domains.

Report
type

Table 2 – Summary of density data collected from technical reports
Density
estimated
Density by
Deposit type
Density
weighted
from
simple
not
density data
average
discussed

Resource
PEA
PFS
Resource
PEA
PFS
Resource
PEA
Resource

Precious metal
Precious metal
Precious metal
Base metal
Base metal
Base metal
Porphyry
Porphyry
Rare metal

4
0
3
0
0
0
1
1
0

14
2
1
3
1
0
4
0
4

4
0
1
3
0
1
1
0
0

0
0
0
0
2
0
0
0
0

Density as
percentage
of assay
data
14
3
3
11
49
100
5
0
24

CONCLUSIONS
Bulk density is a significant and critical component of the resource estimate. Bulk density is used
to converts the estimated volume to tonnes which are reported in the mineral resource and mineral reserve
statements. For mineral deposits that have low metal content and simple mineralogy, estimating bulk
density by calculating an average of all bulk density measurements can be adequate if sufficient data has
been collected and a meaningful average can be estimated. However, each geological domain must be
examined individually and a separate bulk density value must be calculated for each geological domain.
For deposit with more complex mineralogy and where a relationship exists between density and
grade, a simple averaging of bulk density for each geological domain will undoubtedly result in errors in
local bulk density estimation and errors in the reported resource tonnage. A better approach is to estimate
bulk density in the model using similar interpolation parameters applied to grade estimation. For deposits
with high grade and density variability such as base metal or uranium deposit, weighting of grades by
density and estimation of grade times bulk density is preferable for a more accurate resource estimate.

ACKNOWLEDGEMENTS
The author would like to acknowledge SRK Consulting (Canada) Inc. for providing the
opportunity to prepare this paper and all my colleagues in the Vancouver office for providing stimulating
conversation on the topic of bulk density, specifically Marek Nowak for reviewing the document and
providing critical insights. The author also wishes to thank Catherine O’Reilly for the compilation of the
technical reports from SEDAR.
REFERENCES
Dias, P., Costa, J. F., Diedrich, and Koppe, V. (2012). The effect of considering density as weighting factor
when compositing assay grades and as accumulated variable on mining reconciliation. Ninth
International Geostatistics Congress, Oslo, Norway.
Dominy, S. C., Noppé, and Annels, A. E. (2004). Errors and uncertainty in mineral resource and ore
reserves estimation: The importance of getting it right. Exploration Mining Geology Vol. 11, No.
1-4, 77-98.
Lipton, T., (2000). Modelling bulk density: The importance of getting it right. Proceedings, Fourth
International Mining Geology Conference. Australasian Institute of Mining and Metallurgy, 291297.
Lipton, T., (2001). Measurement of bulk density for resource estimation. In A.C. Edwards (Ed.), Mineral
resource and ore reserves estimation – The AusIMM guide to good practice Monograph 23 (pp.
57-66). Melbourne, Australia: Australasian Institute of Mining and Metallurgy
The Northern Miner (1988). Updated Reserve Report in Progress for Ketza River. October 31 – November
6, Volume 74, No. 34
Sinclair. A. J, and Blackwell, G. H. (2002). Applied mineral inventory estimation. Cambridge, United
Kingdom, Cambridge University Press

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