ENERGY BALANCE
5.1 INTRODUCTION
Energy can exist in several forms: heat, mechanical energy, electrical energy, e.t.c. As with mass, energy can be considered to be separately conserved in all but nuclear processes. The conservation of energy, however, differs from that of mass in that energy can be generated (or consumed) in a chemical process. Material can change form, new molecular species can be formed by chemical reaction, but the total mass flow into a process unit must be equal to the flow out at the steady state. The same is not true of energy. The total enthalpy of the outlet streams will not equal that of the inlet streams if energy is generated or consumed in the processes; such as that due to heat of reaction. Talking of energy conservation, it is the total energy that is conserved (Sinnott, 2005). When a process is maintained isothermal, only a material balance is needed to describe the process, unless it is also required to know the net heat transfer for maintaining a constant temperature (Stanley, 1990).
In process design, energy balances are made to determine the energy requirements of the process: the heating, cooling and power required. In plant operation, an energy balance (energy audit) on the plant will show the pattern of energy usage, and suggest areas for conservation and savings. Energy balances can identify equipment with a high energy requirement or large surplus of energy to be removed.
5.2 CONSERVATION OF ENERGY
A general equation can be written for the conservation of energy:
Energy out = Energy in + generation ̶ consumption ̶ accumulation
This is a statement of the first law of thermodynamics. An energy balance can be written for any process step. Chemical reaction will evolve energy (exothermic) or consume energy (endothermic). For steady-state processes the accumulation of both mass and energy will be zero.
Energy can exist in many forms and this, to some extent, makes an energy balance
more complex than a material balance.
5.3 HEATS OF REACTION.
If a process involves chemical reaction, heat will normally have to be added or removed. The amount of heat given out in a chemical reaction depends on the conditions under which the reaction is carried out. The standard heat of reaction (ΔHor) is the heat released when the reaction is carried out under standard conditions: pure components, 1 atm (1.01325bar), temperature usually, but not necessarily, 25oC. (Sinnott, 2005)
5.4 HEATS OF FORMATION.
The standard enthalpy of formation (ΔHof) of a compound is defined as the enthalpy change when one mole of the compound is formed from its constituent elements in the standard state. The standard heat of any reaction can be calculated from the heats of formation, -ΔHof of the products and reactants; if these are available or can be estimated. The relationship between standard heat of reaction and formation is given by: (Sinnott, 2005).
ΔHor = ∑ ΔHof products - ∑ΔHof reactants .........................................................................(5.1)
Where
ΔHof (KJ/day) = Amount (kmol/day) x ΔHof (kJ/kmol) ........................................................(5.2)
and
Amount =Mass/(Molecular weight) ...........................................................................(5.3)
A scale-up factor of 5.8976 is used to multiply all masses of components. This was obtained from the calculation done in chapter four. This means that all the masses calculated for the material balance were computed based on the basis chosen.
∴Mass=Mass basis ×5.8976 ......................................................................... (5.4)
To convert from kcal/mol to kJ/mol,
1 kcal/mol = 4.1868 kJ/mol
= 4.1868 x 1000 kJ/kmol
= 4186.8 kJ/kmol
The values obtained for the heat of reaction are divided by operational time of 8 hours to obtain heat of reaction in kJ/hr. The table below shows the heats of formation of the compounds involved in the material balance equations.
Table 5.1 Heats of Formation of some Compounds at 25oC
Compound Heat of Formation, ΔHor (kcal/mol)
Al(OH)3 -304.8000
Al2(SO4)3.18H20 -2120.0000
Ca(HCO3)2 -460.1300
Ca(OCl)2 -92.6000
Ca(OH)2 -235.5800
CaCl2 -190.6000
CaCO3 -289.5000
CaSO4 -336.5800
CO2 -94.0520
Fe(HCO3)2 -303.5200
Fe(OH)3 -197.3000
H2O -68.3174
H2S -4.7700
Compound Heat of Formation, ΔHor (kcal/mol)
HClO -28.1800
Mg(HCO3)2 -332.1600
Mg(OH)2 -221.9000
MgCl2 -189.7600
MgSO4 -325.4000
Mn(HCO3)2 -317.5400
Mn2O3.H2O -222.9000
Na2CO3 -275.1300
Na2SO4 -330.8200
NaCl -97.3240
O2 0.0000
SO2 -70.94000
Source: (Perry, et al., 1997; Robert,1974) .
5.5 ENERGY BALANCE OVER LIME DOSING AND AERATOR
The reactions that take place at the point of slaked lime - water dosing and at the aerator are combined.
5.5.1 Energy Balance for Iron Bicarbonate Removal
4Fe(HCO3)2(aq) + O2(g) + 4Ca(OH)2(aq) → 4Fe(OH)3(c)↓ + 4CaCO3(c)↓+ 4CO2(g) + 2H2O(l)
Table 5.2 Energy balance for iron bicarbonate removal
Reactants
Component mass (basis), kg/day mass, kg/day molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof,
kJ/kmol Hof,
kJ/day
Fe(HCO3)2 237.7620 1402.2252 178.0 7.8777 -303.5200 -1270777.5360 -10010765.4381
O2 10.6859 63.0212 32.0 1.9694 0.0000 0.0000 0.0000
Ca(OH)2 98.8449 582.9477 74.0 7.8777 -235.5800 -986326.3440 -7769954.8131
∑∆Hof reactants = -17780720.2511
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof,
kJ/kmol
ΔHof,
kJ/day
Fe(OH)3 142.9243 842.9104 107.0 7.8777 -197.3000 -826055.6400 -6507391.1217
CaCO3 133.5742 787.7672 100.0 7.8777 -289.5000 -1212078.6000 -9548357.6723
CO2 58.7726 346.6173 44.0 7.8777 -94.0520 -393776.9136 -3102042.8406
H2O 12.0217 70.8992 18.0 3.9388 -68.3174 -286031.2903 -1126632.4079
∑∆Hof products = -20284424.0425
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= –20,284,424.0425 kJ/day – (–17,780,720.2511 kJ/day)
= – 2,503,703.7914 kJ/day
= – 312962.9739 kJ/hr
5.5.2 Energy Balance for Manganese Bicarbonate Removal
4Mn(HCO3)2(aq) + O2(g) + 4Ca(OH)2(aq) → 2Mn2O3∙H2O(c)↓ + 4CaCO3(c)↓+ 4CO2(g) + 2H2O(l)
Table 5.3 Energy balance for manganese bicarbonate removal
Reactants
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof,
kJ/kmol ΔHof,
kJ/day
Mn(HCO3)2 29.9700 176.7511 177.0 0.9986 -332.1600 -1390687.4880 -1388731.6628
O2 1.3546 7.9889 32.0 0.2497 0.0000 0.0000 0.0000
Ca(OH)2 12.5298 73.8957 74.0 0.9986 -235.5800 -986326.3440 -984936.8032
∑∆Hofreactants =-2373668.4660
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof,
kJ/day
Mn2O3.H2O 14.9003 87.8760 176.0 0.4993 -222.9000 -933237.7200 -465961.4008
CaCO3 16.9322 99.8593 100.0 0.9986 -289.5000 -1212078.6000 -1210373.7232
CO2 7.4502 43.9383 44.0 0.9986 -94.0520 -393776.9136 -393224.7267
H2O 4.5717 26.9621 18.0 1.4979 -68.3174 -286031.2903 -428444.0120
∑ΔHofproducts = -2498003.8627
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= –2,498,003.863 kJ/day – (–2,373,668.466 kJ/day)
= – 124,335.3967 kJ/day
= – 15541.92459 kJ/hr
5.5.3 Energy Balance for Calcium Bicarbonate Removal
Ca(HCO3)2(aq)+ Ca(OH)2(aq) → 2CaCO3(c)↓ + 2H2O(l)
Table 5.4 Energy balance for calcium bicarbonate removal
Reactants
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
Ca(HCO3)2 180.0000 1061.5680 162.0 6.5529 -460.1300 -1926472.2840 -12623958.8246
Ca(OH)2 82.2222 484.9136 74.0 6.5529 -235.5800 -986326.3440 -6463285.1936
∑∆Hof reactants = -19087244.0182
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
CaCO3 222.2222 1310.5776 100.0 13.1058 -289.5000 -1212078.6000 -15885231.1923
H2O 40.0000 235.9040 18.0 13.1058 -68.3174 -286031.2903 -3748662.5284
∑∆Hof products = -19633893.7207
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= – 19,633,893.72 kJ/day – (–19,087,244.0182kJ/day)
= – 546,649.7025 kJ/day
= – 68331.21281 kJ/hr
5.5.4 Energy Balance for Magnesium Bicarbonate Removal
Mg(HCO3)2(aq)+ 2Ca(OH)2(aq) → 2CaCO3(c)↓ +Mg(OH)2 + 2H2O(l)
Table 5.5 Energy balance for calcium bicarbonate removal
Reactants
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
Mg(HCO3)2 140.0000 825.6640 146.0 5.6552 -332.1600 -1390687.4880 -7864661.6034
Ca(OH)2 141.9178 836.9744 74.0 11.3105 -235.5800 -986326.3440 -11155809.6894
∑∆Hofreactants = -19020471.2928
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
CaCO3 191.7808 1131.0464 100.0 11.3105 -289.5000 -1212078.6000 -13709171.9290
Mg(OH)2 55.6164 328.0033 58.0 5.6552 -221.9000 -929050.9200 -5253995.6835
H2O 34.5205 203.5881 18.0 11.3105 -68.3174 -286031.2903 -3235142.6203
∑∆Hof products = -22198310.2328
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= – 22,198,310.2328 kJ/day – (–19,020,471.2928 kJ/day)
= – 3,177,838.94 kJ/day
= – 397229.8675 kJ/hr
5.5.5 Energy Balance for Magnesium Sulphate Removal
MgSO4(aq) + Ca(OH)2(aq) → CaSO4(aq) + Mg(OH)2(c)↓
Table 5.6 Energy balance for magnesium sulphate removal
Reactants
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
MgSO4 39.2000 231.1859 120.0 1.9265 -325.4000 -1362384.7200 -2624701.3741
Ca(OH)2 24.1733 142.5645 74.0 1.9265 -235.5800 -986326.3440 -1900203.7402
∑∆Hof reactants = -4524905.1143
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
CaSO4 44.4267 262.0109 136.0 1.9266 -336.5800 -1409193.1440 -2714882.1491
Mg(OH)2 18.9467 111.7401 58.0 1.9266 -221.9000 -929050.9200 -1789865.5795
∑∆Hof products = -4504747.7286
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= – 4,504,747.729 kJ/day – (– 4,524,905.114 kJ/day)
= 20,157.3857 kJ/day
= 2519.673213 kJ/hr
5.5.6 Energy Balance for Calcium Sulphate Removal
CaSO4(aq) + Na2CO3(aq) → CaCO3(c)↓ + Na2SO4(aq)
Table 5.7 Energy balance for calcium sulphate removal
Reactants
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof,
kJ/kmol ΔHof,
kJ/day
CaSO4 102.3382 603.5498 136.0 4.4379 -336.5800 -1409193.1440 -6253810.2616
Na2CO3 79.7636 470.4138 106.0 4.4379 -275.1300 -1151914.2840 -5112041.3593
∑∆Hof reactants = -11365851.6209
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
CaCO3 75.2487 443.7867 100.0 4.4379 -289.5000 -1212078.6000 -5379044.0218
Na2SO4 106.8531 630.1768 142.0 4.4379 -330.8200 -1385077.1760 -6146785.6442
∑∆Hof products = -11525829.6660
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= – 11,525,829.67 kJ/day – (– 11,365,851.62 kJ/day)
= – 159,978.0451 kJ/day
= – 19997.25564 kJ/hr
5.5.7 Energy Balance for Magnesium Chloride Removal
` MgCl2(aq)+ Ca(OH)2(aq) + Na2CO3(aq) → CaCO3(c)↓ + Mg(OH)2(c)↓ + 2NaCl(aq)
Table 5.8 Energy balance for magnesium chloride removal
Reactants
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof,
kJ/kmol ΔHof,
kJ/day
MgCl2 24.5 144.4912 95.0 1.5210 -189.7600 -794487.1680 -1208383.2030
Ca(OH)2 19.0842 112.5510 74.0 1.5210 -235.5800 -986326.3440 -1500162.0887
Na2CO3 27.3368 161.2215 106.0 1.5210 -275.1300 -1151914.2840 -1752012.8509
∑∆Hof reactants = -4460558.1426
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof,
kJ/kmol ΔHof,
kJ/day
CaCO3 25.7895 152.0962 100.0 1.5210 -289.5000 -1212078.6000 -1843524.9486
Mg(OH)2 14.9579 88.2157 58.0 1.5210 -221.9000 -929050.9200 -1413049.7845
NaCl 30.1737 177.9524 58.5 3.0419 -97.3240 -407476.1232 -1239510.4173
∑∆Hof products =-4496085.1504
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= – 4,496,085.15 kJ/day – (– 4,460,558.143 kJ/day)
= – 35527.0078 kJ/day
= – 4440.875975 kJ/hr
5.5.8 Energy Balance for Calcium Chloride Removal
CaCl2 + Na2CO3 → CaCO3↓ + 2NaCl
5.1 INTRODUCTION
Energy can exist in several forms: heat, mechanical energy, electrical energy, e.t.c. As with mass, energy can be considered to be separately conserved in all but nuclear processes. The conservation of energy, however, differs from that of mass in that energy can be generated (or consumed) in a chemical process. Material can change form, new molecular species can be formed by chemical reaction, but the total mass flow into a process unit must be equal to the flow out at the steady state. The same is not true of energy. The total enthalpy of the outlet streams will not equal that of the inlet streams if energy is generated or consumed in the processes; such as that due to heat of reaction. Talking of energy conservation, it is the total energy that is conserved (Sinnott, 2005). When a process is maintained isothermal, only a material balance is needed to describe the process, unless it is also required to know the net heat transfer for maintaining a constant temperature (Stanley, 1990).
In process design, energy balances are made to determine the energy requirements of the process: the heating, cooling and power required. In plant operation, an energy balance (energy audit) on the plant will show the pattern of energy usage, and suggest areas for conservation and savings. Energy balances can identify equipment with a high energy requirement or large surplus of energy to be removed.
5.2 CONSERVATION OF ENERGY
A general equation can be written for the conservation of energy:
Energy out = Energy in + generation ̶ consumption ̶ accumulation
This is a statement of the first law of thermodynamics. An energy balance can be written for any process step. Chemical reaction will evolve energy (exothermic) or consume energy (endothermic). For steady-state processes the accumulation of both mass and energy will be zero.
Energy can exist in many forms and this, to some extent, makes an energy balance
more complex than a material balance.
5.3 HEATS OF REACTION.
If a process involves chemical reaction, heat will normally have to be added or removed. The amount of heat given out in a chemical reaction depends on the conditions under which the reaction is carried out. The standard heat of reaction (ΔHor) is the heat released when the reaction is carried out under standard conditions: pure components, 1 atm (1.01325bar), temperature usually, but not necessarily, 25oC. (Sinnott, 2005)
5.4 HEATS OF FORMATION.
The standard enthalpy of formation (ΔHof) of a compound is defined as the enthalpy change when one mole of the compound is formed from its constituent elements in the standard state. The standard heat of any reaction can be calculated from the heats of formation, -ΔHof of the products and reactants; if these are available or can be estimated. The relationship between standard heat of reaction and formation is given by: (Sinnott, 2005).
ΔHor = ∑ ΔHof products - ∑ΔHof reactants .........................................................................(5.1)
Where
ΔHof (KJ/day) = Amount (kmol/day) x ΔHof (kJ/kmol) ........................................................(5.2)
and
Amount =Mass/(Molecular weight) ...........................................................................(5.3)
A scale-up factor of 5.8976 is used to multiply all masses of components. This was obtained from the calculation done in chapter four. This means that all the masses calculated for the material balance were computed based on the basis chosen.
∴Mass=Mass basis ×5.8976 ......................................................................... (5.4)
To convert from kcal/mol to kJ/mol,
1 kcal/mol = 4.1868 kJ/mol
= 4.1868 x 1000 kJ/kmol
= 4186.8 kJ/kmol
The values obtained for the heat of reaction are divided by operational time of 8 hours to obtain heat of reaction in kJ/hr. The table below shows the heats of formation of the compounds involved in the material balance equations.
Table 5.1 Heats of Formation of some Compounds at 25oC
Compound Heat of Formation, ΔHor (kcal/mol)
Al(OH)3 -304.8000
Al2(SO4)3.18H20 -2120.0000
Ca(HCO3)2 -460.1300
Ca(OCl)2 -92.6000
Ca(OH)2 -235.5800
CaCl2 -190.6000
CaCO3 -289.5000
CaSO4 -336.5800
CO2 -94.0520
Fe(HCO3)2 -303.5200
Fe(OH)3 -197.3000
H2O -68.3174
H2S -4.7700
Compound Heat of Formation, ΔHor (kcal/mol)
HClO -28.1800
Mg(HCO3)2 -332.1600
Mg(OH)2 -221.9000
MgCl2 -189.7600
MgSO4 -325.4000
Mn(HCO3)2 -317.5400
Mn2O3.H2O -222.9000
Na2CO3 -275.1300
Na2SO4 -330.8200
NaCl -97.3240
O2 0.0000
SO2 -70.94000
Source: (Perry, et al., 1997; Robert,1974) .
5.5 ENERGY BALANCE OVER LIME DOSING AND AERATOR
The reactions that take place at the point of slaked lime - water dosing and at the aerator are combined.
5.5.1 Energy Balance for Iron Bicarbonate Removal
4Fe(HCO3)2(aq) + O2(g) + 4Ca(OH)2(aq) → 4Fe(OH)3(c)↓ + 4CaCO3(c)↓+ 4CO2(g) + 2H2O(l)
Table 5.2 Energy balance for iron bicarbonate removal
Reactants
Component mass (basis), kg/day mass, kg/day molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof,
kJ/kmol Hof,
kJ/day
Fe(HCO3)2 237.7620 1402.2252 178.0 7.8777 -303.5200 -1270777.5360 -10010765.4381
O2 10.6859 63.0212 32.0 1.9694 0.0000 0.0000 0.0000
Ca(OH)2 98.8449 582.9477 74.0 7.8777 -235.5800 -986326.3440 -7769954.8131
∑∆Hof reactants = -17780720.2511
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof,
kJ/kmol
ΔHof,
kJ/day
Fe(OH)3 142.9243 842.9104 107.0 7.8777 -197.3000 -826055.6400 -6507391.1217
CaCO3 133.5742 787.7672 100.0 7.8777 -289.5000 -1212078.6000 -9548357.6723
CO2 58.7726 346.6173 44.0 7.8777 -94.0520 -393776.9136 -3102042.8406
H2O 12.0217 70.8992 18.0 3.9388 -68.3174 -286031.2903 -1126632.4079
∑∆Hof products = -20284424.0425
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= –20,284,424.0425 kJ/day – (–17,780,720.2511 kJ/day)
= – 2,503,703.7914 kJ/day
= – 312962.9739 kJ/hr
5.5.2 Energy Balance for Manganese Bicarbonate Removal
4Mn(HCO3)2(aq) + O2(g) + 4Ca(OH)2(aq) → 2Mn2O3∙H2O(c)↓ + 4CaCO3(c)↓+ 4CO2(g) + 2H2O(l)
Table 5.3 Energy balance for manganese bicarbonate removal
Reactants
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof,
kJ/kmol ΔHof,
kJ/day
Mn(HCO3)2 29.9700 176.7511 177.0 0.9986 -332.1600 -1390687.4880 -1388731.6628
O2 1.3546 7.9889 32.0 0.2497 0.0000 0.0000 0.0000
Ca(OH)2 12.5298 73.8957 74.0 0.9986 -235.5800 -986326.3440 -984936.8032
∑∆Hofreactants =-2373668.4660
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof,
kJ/day
Mn2O3.H2O 14.9003 87.8760 176.0 0.4993 -222.9000 -933237.7200 -465961.4008
CaCO3 16.9322 99.8593 100.0 0.9986 -289.5000 -1212078.6000 -1210373.7232
CO2 7.4502 43.9383 44.0 0.9986 -94.0520 -393776.9136 -393224.7267
H2O 4.5717 26.9621 18.0 1.4979 -68.3174 -286031.2903 -428444.0120
∑ΔHofproducts = -2498003.8627
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= –2,498,003.863 kJ/day – (–2,373,668.466 kJ/day)
= – 124,335.3967 kJ/day
= – 15541.92459 kJ/hr
5.5.3 Energy Balance for Calcium Bicarbonate Removal
Ca(HCO3)2(aq)+ Ca(OH)2(aq) → 2CaCO3(c)↓ + 2H2O(l)
Table 5.4 Energy balance for calcium bicarbonate removal
Reactants
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
Ca(HCO3)2 180.0000 1061.5680 162.0 6.5529 -460.1300 -1926472.2840 -12623958.8246
Ca(OH)2 82.2222 484.9136 74.0 6.5529 -235.5800 -986326.3440 -6463285.1936
∑∆Hof reactants = -19087244.0182
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
CaCO3 222.2222 1310.5776 100.0 13.1058 -289.5000 -1212078.6000 -15885231.1923
H2O 40.0000 235.9040 18.0 13.1058 -68.3174 -286031.2903 -3748662.5284
∑∆Hof products = -19633893.7207
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= – 19,633,893.72 kJ/day – (–19,087,244.0182kJ/day)
= – 546,649.7025 kJ/day
= – 68331.21281 kJ/hr
5.5.4 Energy Balance for Magnesium Bicarbonate Removal
Mg(HCO3)2(aq)+ 2Ca(OH)2(aq) → 2CaCO3(c)↓ +Mg(OH)2 + 2H2O(l)
Table 5.5 Energy balance for calcium bicarbonate removal
Reactants
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
Mg(HCO3)2 140.0000 825.6640 146.0 5.6552 -332.1600 -1390687.4880 -7864661.6034
Ca(OH)2 141.9178 836.9744 74.0 11.3105 -235.5800 -986326.3440 -11155809.6894
∑∆Hofreactants = -19020471.2928
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
CaCO3 191.7808 1131.0464 100.0 11.3105 -289.5000 -1212078.6000 -13709171.9290
Mg(OH)2 55.6164 328.0033 58.0 5.6552 -221.9000 -929050.9200 -5253995.6835
H2O 34.5205 203.5881 18.0 11.3105 -68.3174 -286031.2903 -3235142.6203
∑∆Hof products = -22198310.2328
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= – 22,198,310.2328 kJ/day – (–19,020,471.2928 kJ/day)
= – 3,177,838.94 kJ/day
= – 397229.8675 kJ/hr
5.5.5 Energy Balance for Magnesium Sulphate Removal
MgSO4(aq) + Ca(OH)2(aq) → CaSO4(aq) + Mg(OH)2(c)↓
Table 5.6 Energy balance for magnesium sulphate removal
Reactants
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
MgSO4 39.2000 231.1859 120.0 1.9265 -325.4000 -1362384.7200 -2624701.3741
Ca(OH)2 24.1733 142.5645 74.0 1.9265 -235.5800 -986326.3440 -1900203.7402
∑∆Hof reactants = -4524905.1143
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
CaSO4 44.4267 262.0109 136.0 1.9266 -336.5800 -1409193.1440 -2714882.1491
Mg(OH)2 18.9467 111.7401 58.0 1.9266 -221.9000 -929050.9200 -1789865.5795
∑∆Hof products = -4504747.7286
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= – 4,504,747.729 kJ/day – (– 4,524,905.114 kJ/day)
= 20,157.3857 kJ/day
= 2519.673213 kJ/hr
5.5.6 Energy Balance for Calcium Sulphate Removal
CaSO4(aq) + Na2CO3(aq) → CaCO3(c)↓ + Na2SO4(aq)
Table 5.7 Energy balance for calcium sulphate removal
Reactants
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof,
kJ/kmol ΔHof,
kJ/day
CaSO4 102.3382 603.5498 136.0 4.4379 -336.5800 -1409193.1440 -6253810.2616
Na2CO3 79.7636 470.4138 106.0 4.4379 -275.1300 -1151914.2840 -5112041.3593
∑∆Hof reactants = -11365851.6209
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof, kJ/kmol ΔHof, kJ/day
CaCO3 75.2487 443.7867 100.0 4.4379 -289.5000 -1212078.6000 -5379044.0218
Na2SO4 106.8531 630.1768 142.0 4.4379 -330.8200 -1385077.1760 -6146785.6442
∑∆Hof products = -11525829.6660
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= – 11,525,829.67 kJ/day – (– 11,365,851.62 kJ/day)
= – 159,978.0451 kJ/day
= – 19997.25564 kJ/hr
5.5.7 Energy Balance for Magnesium Chloride Removal
` MgCl2(aq)+ Ca(OH)2(aq) + Na2CO3(aq) → CaCO3(c)↓ + Mg(OH)2(c)↓ + 2NaCl(aq)
Table 5.8 Energy balance for magnesium chloride removal
Reactants
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof,
kJ/kmol ΔHof,
kJ/day
MgCl2 24.5 144.4912 95.0 1.5210 -189.7600 -794487.1680 -1208383.2030
Ca(OH)2 19.0842 112.5510 74.0 1.5210 -235.5800 -986326.3440 -1500162.0887
Na2CO3 27.3368 161.2215 106.0 1.5210 -275.1300 -1151914.2840 -1752012.8509
∑∆Hof reactants = -4460558.1426
Products
Component Mass (basis), kg/day Mass, kg/day Molar mass, kg/kmol Amount, kmol/day ΔHof, kcal/mol ΔHof,
kJ/kmol ΔHof,
kJ/day
CaCO3 25.7895 152.0962 100.0 1.5210 -289.5000 -1212078.6000 -1843524.9486
Mg(OH)2 14.9579 88.2157 58.0 1.5210 -221.9000 -929050.9200 -1413049.7845
NaCl 30.1737 177.9524 58.5 3.0419 -97.3240 -407476.1232 -1239510.4173
∑∆Hof products =-4496085.1504
ΔHor = ∑ ΔHof products - ∑ ΔHof reactants
= – 4,496,085.15 kJ/day – (– 4,460,558.143 kJ/day)
= – 35527.0078 kJ/day
= – 4440.875975 kJ/hr
5.5.8 Energy Balance for Calcium Chloride Removal
CaCl2 + Na2CO3 → CaCO3↓ + 2NaCl
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