Lime kiln principles and operations

HEAT RATE CALCULATION NOMENCLATURE

G_f = Fuel flow rate

G_CaO = CaO production rate G_CO2 = CO2 flow rate G_CaCO3 = CaCO3 flow rate G_i = Inerts flow rate
G_w = Flow rate of water in mud G_d = Dust flow rate
G_a = Air flow rate
G_cp = Combustion product flow rate HR = Kiln heat rate
∆Hr = Heat of reaction of CaCO₃ => CaO + CO₂, at T_ref HHV = Higher heating value
LHV = Lower heating value T_p = Kiln product temperature T_ge = Kiln exit gas temperature T_ref = Reference temperature
Cp_i = Specific heat of component i h_i = Heat in component i above T_ref f_LHV = Fraction of HHV in LHV
f_cp = Fraction of HHV in combustion products at T_ge AFS = Stoichiometric air-to-fuel ratio
e = Excess air s = Mud solids
a = Lime availability d = Dust loss
h_fg = Enthalpy of vaporization of water Q_sh = Shell heat loss


MASS FLOW RELATIONSHIPS
_Gm _{ G}CaO 1  0.786 a 1
a 1  d
_Gd _{ G}CaO 1  0.786a d
a 1 d
_Gw _{ G}CaO 1  0.786a 1 1  s
a 1  d s

a
^Gi ^{ G}CaO ^{1  a}



56
^GCO2 ^{ G}CaO ^44
G_cp ^{ G}_f ^{1  1  e AFS}





FUEL HEATING VALUE LOSSES

• 
  Loss due to use of higher heating value
  

LHV
f  LHV HHV

• Loss due to flow of combustion products

^{1  1  e AFS}^Cp_{cp }^T_ge ^{ T}_{ref }

f _cp 
HHV

KILN ENERGY BALANCE
^Gf ^{HHV f} LHV ^{ f} cp ^{ G}CaO ^Hr ^{ Cp}CaO ^T p ^{ T}ref <sup>


G</sup>CO 2^CpCO2 ^T ge ^{ T}ref ^


G_iCp_{i }T _p  T_{ref }


^Gw ^h fg ^{ Cp}w ^Tge ^{ T}ref ^


G_dCp_{d }T_ge  T_{ref } Q_sh

• Heat rate definition

_{HR } G_f HHV
^GCaO


HEAT RATE CALCULATION
(Heat loss method)
HR_f _LHV  f _{cp } _H_r  Cp_{CaO }T _p  T_{ref }

• 
  
  56
  ^{44 Cp}CO2 ^Tge ^{ T}_ref ^
  

a
^{1  a} Cp_{i }T _p  T_{ref 
}1  0.786a 1 1  s _h fg _{ Cp}w _Tge _{ T}ref _
a 1  d s

_1  0.786a d _{Cp T  T
} ^Qsh

a 1  d
d ge
ref
^GCaO

HEAT RATE CALCULATION PARAMETERS

FUEL CONSTANTS
	Nat. gas	Fuel oil
HHV	5.37E+07	4.27E+07	J/kg
LHV	4.84E+07	4.07E+07	J/kg
AFS	16.80	13.44

EXCESS AIR "CONSTANTS"
Dry basis factor	5.40	5.62
Wet basis factor	8.96	8.60
Assumed HR	7		GJ/tonne

PROPERTIES
Comb. prod. specific heat	Cpcp	1,267	J/kg/°C
Reburn specific heat	^CpCaO	989	J/kg/°C
CO2 specific heat	^CpCO2	919	J/kg/°C
Inerts specific heat	Cpi	1,046	J/kg/°C
Steam specific heat	Cps	1,991	J/kg/°C
Heat of calcination	∆Hr	3,270,045	J/kg
Enthalpy of vaporization	^hfg	2,439,465	J/kg

EXCESS AIR CALCULATION

_{e } ^XO2
1  4.76_X_{O2 }
 factor 

• Fuel oil with dry-basis O₂ probe

^{factor  }^{4. 53  5.65} ^
 HR 

• 
  Fuel oil with wet-basis O₂ probe
  

 _

^ 1  0.56^{1  a  }

factor  ^4.99  ^{5.65 }1  5.56^{ a  1  s }


^ HR _

_ 

_ 1  d






_ s _

 _

• Natural gas with dry-basis O₂ probe

^{factor  }^{4. 28  5.82} ^
 HR 

• 
  Natural gas with wet-basis O₂ probe
  

^{  } 1  0.56^{1  a  }

factor  ^5. 24  ^{5.82 }1  5.56^{ a  1  s }


^ HR _

_ 

_ 1  d






_ s _

 _

SHELL HEAT LOSS CALCULATION

• 
  Convection, W/m²
  

c sh sh
^{q  1.175}_^{22.75 * V 2  1.8 *} ^{T  25}_^0.35 ^{T  25}

• Radiation, W/m²

^q_r ^{ 5.668 x108 sh} _^T_sh ^{ 273}^{4  2984}

• Shell heat loss, W

^{Qsh  D}_^x ^{qc  qr} _i
i

where:

V = Wind velocity, m/s

T_sh = Shell temperature, °C

ε_sh = Shell emissivity

D = Kiln outside diameter, m

2.2-