594 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
could be used to assess the water loss potential of different
equipment and circuits.
BACKGROUND
Estimating water loss in an open body of water scenario
comes down to the use of Dalton relationship (ETB, 2023
Feistel &Hellmuth, 2023 Headrick, 1967 Jensen, 2010):
m x xh
evap s HAsl =-o ^(1)
where:
25 19vh H =+^(2)
and:
v =velocity of air over water surface [m/s],
Asl =area of water surface [m2],
xs =humidity ratio in saturated air at the surface
water temperature [kg/kg],
x =humidity ratio in the air [kg/kg].
The resulting energy lost by evaporation can now be deter-
mined as:
Q m h
evap evap evap =o (3)
where:
hevap =heat of vaporization of water [kJ/kg]
ESTIMATING WATER LOSS
Before developing a model to estimate water loss through
evaporation in mineral processing, it is important to under-
line that evaporation is a natural and ever-present phenom-
enon. At any given location, evaporation is a function of
local water temperatures, humidity levels, water surface
area, wind speeds and solar intensity.
Mining activities will bring increased water surface area
through the use of holding tanks, flotation cells, thicken-
ers, any equipment presenting a free surface which includes
tailings facilities. Assuming that the temperatures of all of
the bodies of water in a plant are the same and equal to that
of the ambient outside temperature of the tailings pond or
raw water tank, the Dalton relationship could be used to
estimate water evaporation rates as illustrated in Gunson
et al. (2012).
However, water and ore (slurry) temperatures will
increase in comminution circuits due to the heat gener-
ated in grinding. This added heat will increase water loss
through evaporation beyond what the Dalton relationship
estimates.
To estimate the water loss through evaporation related
to the heat generated comminution, a control volume
needs to be defined around a system such as a mineral pro-
cessing plant along with all mass and energy inputs and
outputs across the control volume boundary as illustrated
in Figure 1. In the following development, the plant con-
trol volume excludes the concentrate and the tailings.
In the case of a mineral processing plant, mass and
energy balances over the control volume are defined as
follows:
W Esolar Q h mw2 hw2h
h m h
.c v. lost ore2
ore1 ore1 w w1
2
1
+-=+
-+
o o
o ^mo
^more
h
(4)
where:
W
.c v.
o =work input to the control volume [kJ/s
or kW],
E
solar =solar energy input to the control volume
[kJ/s or kW],
Qlost o =energy lost to the environment [kJ/s
or kW],
,m m
ore1 ore2
o =ore mass flow rate [kg/s],
hore1,hore2 =ore feed and discharge enthalpy respec-
tively [kJ/kg],
,m m
w w2 1 o =water mass flow rate [kg/s],
hw1,hw2 =water feed and discharge enthalpy respec-
tively [kJ/kg].
and:
Q Q Q
lost heat evap =+o o o (5)
The mass balance over the control volume is defined as:
m more more2
ore 1 ==o (6)
m mw2 mevap
w 1 =+o (7)
Assuming (assumption #1) that the mass loss through evap-
oration (mevap )is small as compared to the total water used
Figure 1. Generic control volume around a system
could be used to assess the water loss potential of different
equipment and circuits.
BACKGROUND
Estimating water loss in an open body of water scenario
comes down to the use of Dalton relationship (ETB, 2023
Feistel &Hellmuth, 2023 Headrick, 1967 Jensen, 2010):
m x xh
evap s HAsl =-o ^(1)
where:
25 19vh H =+^(2)
and:
v =velocity of air over water surface [m/s],
Asl =area of water surface [m2],
xs =humidity ratio in saturated air at the surface
water temperature [kg/kg],
x =humidity ratio in the air [kg/kg].
The resulting energy lost by evaporation can now be deter-
mined as:
Q m h
evap evap evap =o (3)
where:
hevap =heat of vaporization of water [kJ/kg]
ESTIMATING WATER LOSS
Before developing a model to estimate water loss through
evaporation in mineral processing, it is important to under-
line that evaporation is a natural and ever-present phenom-
enon. At any given location, evaporation is a function of
local water temperatures, humidity levels, water surface
area, wind speeds and solar intensity.
Mining activities will bring increased water surface area
through the use of holding tanks, flotation cells, thicken-
ers, any equipment presenting a free surface which includes
tailings facilities. Assuming that the temperatures of all of
the bodies of water in a plant are the same and equal to that
of the ambient outside temperature of the tailings pond or
raw water tank, the Dalton relationship could be used to
estimate water evaporation rates as illustrated in Gunson
et al. (2012).
However, water and ore (slurry) temperatures will
increase in comminution circuits due to the heat gener-
ated in grinding. This added heat will increase water loss
through evaporation beyond what the Dalton relationship
estimates.
To estimate the water loss through evaporation related
to the heat generated comminution, a control volume
needs to be defined around a system such as a mineral pro-
cessing plant along with all mass and energy inputs and
outputs across the control volume boundary as illustrated
in Figure 1. In the following development, the plant con-
trol volume excludes the concentrate and the tailings.
In the case of a mineral processing plant, mass and
energy balances over the control volume are defined as
follows:
W Esolar Q h mw2 hw2h
h m h
.c v. lost ore2
ore1 ore1 w w1
2
1
+-=+
-+
o o
o ^mo
^more
h
(4)
where:
W
.c v.
o =work input to the control volume [kJ/s
or kW],
E
solar =solar energy input to the control volume
[kJ/s or kW],
Qlost o =energy lost to the environment [kJ/s
or kW],
,m m
ore1 ore2
o =ore mass flow rate [kg/s],
hore1,hore2 =ore feed and discharge enthalpy respec-
tively [kJ/kg],
,m m
w w2 1 o =water mass flow rate [kg/s],
hw1,hw2 =water feed and discharge enthalpy respec-
tively [kJ/kg].
and:
Q Q Q
lost heat evap =+o o o (5)
The mass balance over the control volume is defined as:
m more more2
ore 1 ==o (6)
m mw2 mevap
w 1 =+o (7)
Assuming (assumption #1) that the mass loss through evap-
oration (mevap )is small as compared to the total water used
Figure 1. Generic control volume around a system