XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 595
in mineral processing, it is possible to approximately equate
the output water rate with the input water rate:
m mw1 mw2
w ,=o (8)
Furthermore, it can be assumed (assumption #2) that the
temperatures of the input ore and water as well as the tem-
peratures of the output ore and water (slurry) are equal:
T Tore1 Tw1
1 ,=(9)
T T T
ore2 w2 2 ==(10)
Assuming (assumption #3) constant pressure, an incom-
pressible fluid and solid in the slurry, it is possible to reduce
the energy balance to the following:
W E Q c m c
T
.c v. solar lost ore ore water water
2 1 #^T
+-=+
-
o o ^m
h
h
(11)
where:
core, cwater =specific heats of the ore and water (Waples
and Waples, 2004) [kJ/kg-K].
Solving the energy balance (equ 4) for the energy lost term
also defines energy lost:
Q W E
m core m cwaterh^T T
.lost c v. solar
ore water 2 1
=+
-+-
o o
o o ^h
(12)
For the control volume capturing the plant, it will be
assumed (assumption #4) that the temperature of the con-
centrate and tailings that are being discharged from the
plant are at the same temperature and that temperature
equals the temperature of the input materials (T2 =T1).
Consequently, the energy lost equation (12) can be equated
with equation (5) and equation (3) can be substituted into
the equation giving:
Q Wc.v. E Qheat m hevap
lost solar evap =+=+o o o o o (13)
At this point, one can assume (assumption #5) that all
energy lost (Qlost o )is only through mass transfer due to
evaporation (i.e., energy lost by heat transfer, Qheat o ,is
equal to zero). Knowing that energy lost by evaporation is
a function of evaporation enthalpy and mass loss rate, it is
then possible to reformulate the following relationship for
potential water loss of a given mineral processing plant as a
function of the energy input into the plant control volume:
mevap h
W E
.
evap
c v. solar =
+o ^h (14)
Evaporation enthalpy of water is a function of water tem-
perature. However, between 0C and 100C, it only varies by
about 10%. Consequently, the value used for evaporation
enthalpy (at 0C) is 2500 kJ/kg.
With equation (14) and evaporation enthalpy, it is pos-
sible to revisit energy capture mill data illustrated in previ-
ous works (Radziszewski, 2013 Radziszewski and Hewitt,
2015 Bouchard et al., 2019) and determine the potential
water loss in these plants due to evaporation as illustrated in
Table 1. Note that in these calculations solar energy input
is considered negligible and input energy to heat the slurry
in comminution is considered to be 80% (Bouchard et al.,
2019) of the input mill electrical energy.
Table 1. Potential Water Loss estimates
Parameter Units Brunswick* Cadia* MIDUK* Raglan†
Agnico
Eagle
Goldex‡
Canadian
Malartic‡
New
Afton‡
SAG mill* MW 7.3 19 3.5 2.258 3.357 19.4 5.22
Ball mill* MW 16 6 1.853 3.357 35.7 5.22
Total input power MW 7.3 35 9.5 4.111 6.714 55.1 10.44
Heating efficiency %80
Heat lost kW 5840 28000 7600 3288.8 5371.2 44080 8352
Evaporation enthalpy @0C kJ/kg 2500
Evaporation enthalpy @0C kWh/kg 0.69
Potential water loss m3/hr 8.41 40.32 10.94 4.74 7.73 63.48 12.03
Plant ore feed rate* t/day 10000 49560 15000 4440 5200 55000 15000
Specific water loss m3/t 0.0202 0.0195 0.0175 0.0256 0.0418 0.3431 0.0650
Source:
*Radziszewski, 2013
† Radziszewski, Hewit, 2015
‡ Bouchard et al., 2019
in mineral processing, it is possible to approximately equate
the output water rate with the input water rate:
m mw1 mw2
w ,=o (8)
Furthermore, it can be assumed (assumption #2) that the
temperatures of the input ore and water as well as the tem-
peratures of the output ore and water (slurry) are equal:
T Tore1 Tw1
1 ,=(9)
T T T
ore2 w2 2 ==(10)
Assuming (assumption #3) constant pressure, an incom-
pressible fluid and solid in the slurry, it is possible to reduce
the energy balance to the following:
W E Q c m c
T
.c v. solar lost ore ore water water
2 1 #^T
+-=+
-
o o ^m
h
h
(11)
where:
core, cwater =specific heats of the ore and water (Waples
and Waples, 2004) [kJ/kg-K].
Solving the energy balance (equ 4) for the energy lost term
also defines energy lost:
Q W E
m core m cwaterh^T T
.lost c v. solar
ore water 2 1
=+
-+-
o o
o o ^h
(12)
For the control volume capturing the plant, it will be
assumed (assumption #4) that the temperature of the con-
centrate and tailings that are being discharged from the
plant are at the same temperature and that temperature
equals the temperature of the input materials (T2 =T1).
Consequently, the energy lost equation (12) can be equated
with equation (5) and equation (3) can be substituted into
the equation giving:
Q Wc.v. E Qheat m hevap
lost solar evap =+=+o o o o o (13)
At this point, one can assume (assumption #5) that all
energy lost (Qlost o )is only through mass transfer due to
evaporation (i.e., energy lost by heat transfer, Qheat o ,is
equal to zero). Knowing that energy lost by evaporation is
a function of evaporation enthalpy and mass loss rate, it is
then possible to reformulate the following relationship for
potential water loss of a given mineral processing plant as a
function of the energy input into the plant control volume:
mevap h
W E
.
evap
c v. solar =
+o ^h (14)
Evaporation enthalpy of water is a function of water tem-
perature. However, between 0C and 100C, it only varies by
about 10%. Consequently, the value used for evaporation
enthalpy (at 0C) is 2500 kJ/kg.
With equation (14) and evaporation enthalpy, it is pos-
sible to revisit energy capture mill data illustrated in previ-
ous works (Radziszewski, 2013 Radziszewski and Hewitt,
2015 Bouchard et al., 2019) and determine the potential
water loss in these plants due to evaporation as illustrated in
Table 1. Note that in these calculations solar energy input
is considered negligible and input energy to heat the slurry
in comminution is considered to be 80% (Bouchard et al.,
2019) of the input mill electrical energy.
Table 1. Potential Water Loss estimates
Parameter Units Brunswick* Cadia* MIDUK* Raglan†
Agnico
Eagle
Goldex‡
Canadian
Malartic‡
New
Afton‡
SAG mill* MW 7.3 19 3.5 2.258 3.357 19.4 5.22
Ball mill* MW 16 6 1.853 3.357 35.7 5.22
Total input power MW 7.3 35 9.5 4.111 6.714 55.1 10.44
Heating efficiency %80
Heat lost kW 5840 28000 7600 3288.8 5371.2 44080 8352
Evaporation enthalpy @0C kJ/kg 2500
Evaporation enthalpy @0C kWh/kg 0.69
Potential water loss m3/hr 8.41 40.32 10.94 4.74 7.73 63.48 12.03
Plant ore feed rate* t/day 10000 49560 15000 4440 5200 55000 15000
Specific water loss m3/t 0.0202 0.0195 0.0175 0.0256 0.0418 0.3431 0.0650
Source:
*Radziszewski, 2013
† Radziszewski, Hewit, 2015
‡ Bouchard et al., 2019