Component Molecular mass
(kg kmol-1) Component Molecular mass
(kg kmol-1)
Na+ 23 NaHCO3 84
Ca2+ 40 Na2CO3 106
Cl- 35.5 CO2 44
NaCl 58.5 H2O 18
CaCl2 111 CaCO3 100
Table 1: Relative molecular mass values for all components in system
Data was taken from Tuesday 11:28-11:40. Flow rates and temperatures throughout this period were fairly constant and so the mean values were found using the density of water at the relevant temperature (it was assumed that all streams in the process have the density of water). Data for the density of water was taken from Perry (1999). An example calculation for the mean product flow rate is shown below:
m ̇=ρV ̇
m ̇=(4.63*60*991.77)/1000=275.7 kg h^(-1)
A mass balance was then carried out on the whole system. The product specification was taken as 1% w/w Na+. From this, the amount of feedstock added, the amount and composition of material leaving the reactor and the composition of the recycle stream were found:
Figure 1: Block diagram of overall process
Assuming the product was on specification (1% w/w Na+), the mass of sodium ions in the product can be obtained by simply finding 1% of the total mass flow of product (2.755 kg h-1). Converting to molar flow rate using the molecular weight of sodium ions, the amount of chloride ions was found using a stoichiometric balance.
2NaHCO3 Na2CO3 + H2O + CO2 (1)
Na2CO3 + CaCl2 CaCO3 + 2NaCl (2)
n ̇=m ̇/RMM=2.755/23=0.12 kmol h^(-1)
One mole of chloride ions are bonded to one mole of sodium ions. Therefore, there is the same amount of chloride ions as sodium ions in the final product. This was converted to a mass flow rate, using the relative molecular mass as before, and found the mass of chloride ions in the final product as 4.255 kg h-1. As all the chlorine in the system was inputted via the feedstock and exited in the product, the flow rate of feedstock was obtained by performing a component mass balance on chlorine. Chlorine makes up 60.6% w/w of NaCl and 63.9% w/w CaCl2 and the feedstock contamination was taken to be 5% w/w CaCl2.
4.255=(0.95×0.606×S)+(0.05×0.639×S)
Rearranging for the feed rate of Sodical, S:
S=7 kg h^(-1)
The amount of CaCl2 in the Sodical was found, using the contamination, to be 0.35 kg h-1 (0.01 kmol h-1). Using a stoichiometric balance, the amount of dosing agent required and water, sodium chloride, carbon dioxide and calcium carbonate produced were found. The results are shown below:
Sodical feed rate NaCl feed rate CaCl2 feed rate NaHCO3 feed rate Solid feed rate H20 produced
(kg h-1) 7.00 6.64 0.35 1.65 8.65 0.18
(kmol h-1) 0.11 0.01 0.02 0.01 H20 required Total feed rate CO2 produced CaCO3 produced NaCl produced Na2CO3 produced
(kg h-1) 268.51 277.16 0.43 0.10 1.15 1.04
(kmol h-1) 14.92 0.01 0.01 0.02 0.01
Table 2: Feed and production rates in RV1
In order to find the flow rates on every line of the system four equations were derived:
b=r+Y (a)
0.2b=e+r (b)
x=r/R (c)
x=e/(e+P) (d)
Equation (a) was substituted into equation (b) and rearranged to make r the subject:
r=(0.2Y-e)/0.8 (e)
Equations (c) and (d) were set equal to one another and equation (e) substituted in:
r/R=e/(e+P)=(0.2Y-e)/0.8R (f)
The equation for (f) was solved for e and produced the following equation:
0.05e^2-e(0.05Y-0.05P-0.95R)-0.05YP=0 (g)
Substituting in all known values, R=280.2 kg h-1, P=275.7 kg h-1, Y=0.1 kg h-1, and solving the quadratic equation, e was found to be 0.025 kg h-1.
Summing e and P gave E as 275.72 kg h-1. The mole fraction of calcium carbonate in stream E was found, using equation (d), to be 0.0009. This mole fraction is assumed to be the same in streams R and D. Consequently, the amount of CaCO3 in the recycle stream, r, was found by multiplying the recycle rate by the mole fraction of CaCO3. The value obtained was approximately 0.025 kg h-1.
The amount of CaCO3 exiting RV1, b, could then be found by summing the amount of CaCO3 in the recycle stream and the amount produced in RV1. This value was found as 1.01 kg h-1. Assuming an efficiency of PF1 of 95%, the amount of CaCO3 after PF1, d, was found to be 0.05 kg h-1 meaning the amount of CaCO3 removed on PF1, c, was 0.96 kg h-1.
Using the calculated values above, the composition flows of all streams were obtained. The composition flows for stream D were calculated to be:
NaCl H20 CaCO3 Stream D
(kg h-1) 7.012 268.69 0.025 275.73
(kmol h-1) 0.120 14.93 2.55E-04 15.05
(mole fraction) 0.025 0.974 9.09E-05
Table 3: Stream D flow rates and composition
Assuming the same mole fractions in stream R, the flow rates for each component were calculated, as the recycle rate, R, was already known. The results are shown below:
NaCl H20 CaCO3 Stream R
(kg h-1) 7.13 273.01 0.025 280.16
(kmol h-1) 0.122 15.17 2.55E-04 15.29
(mole fraction) 0.025 0.974 9.09E-05
Table 4: Stream R flow rates and composition
The flow rates for stream B were calculated using the known flow rates of stream F and stream R and also the amount of each component produced in RV1. After calculating the flow rates, the mole fraction of each component was found. The results are shown below:
NaCl H20 CaCO3 Stream B
(kg h-1) 14.92 541.70 1.01 557.63
(kmol h-1) 0.255 30.09 0.01 30.36
(mole fraction) 0.027 0.971 1.8E-03
Table 5: Stream B flow rates and composition
It was not necessary, for the energy balance on RV1, to calculate the component flows and mole fractions of stream D, for a purpose other than confirmation of the correct mass balance calculation. This confirmatory balance was carried out, and was found to be correct. This calculation is not shown in the report for the reason mentioned above.
A mass balance was then carried out on the reactor, RV1 using the boundaries shown in Figure 2:
Figure 2: Reactor, RV1 inlet and outlet streams
Specific heat capacity data was collected from Perry (1999) and is summarised below. The units of the collected data vary for different components:
Component Specific heat capacity
(cal mol-1 K-1) Component Specific heat capacity
(kJ kg-1 K-1)
NaCl 10.79 + 0.0042T H20 4.178
CO2 10.34 + 0.00274T – 195500T-2 NaHCO3 1.04277
CaCO3 19.68 + 0.01189T – 307600T-2
CaCl2 16.9 + 0.00386T
Na2CO3 28.9
Table 6: Specific heat capacity values for all components in RV1 mass balance
The specific heat capacity for each component in each stream of the mass balance was found using a mean temperature between the stream temperature and the datum temperature (25°C). The value obtained was then converted from cal mol-1 K-1 to SI units (kJ kg-1 K-1) by multiplying by a conversion factor of 4.186 and dividing by the appropriate molecular mass. The example shown below is for NaCl in the recycle stream entering RV1 (T = 345 K, RxNaCl=7.125 kg h-1):
The value obtained for specific heat capacity was then multiplied by the difference between the stream temperature and the datum temperature and the component mass flow rate. The result shows the enthalpy for the stream component in kJ h-1:
H_((NaCl),R)=0.87×7.125×(345-298)=292 kJ h^(-1)
The sum of all component enthalpies is taken to find the total stream enthalpy and repeated for all streams entering and leaving the reactor RV1. A summary table of results is shown below:
Total enthalpy of stream (kJ h-1)
Feedstock in H2O in Recycle in Reactor exit CO2 exit
0.00 13770.80 54130.62 107475.50 18.16
Table 7: Enthalpies of each stream of mass balance of RV1
In order to complete the energy balance for RV1 the heat of reaction and heat of solution taking place in the vessel had to be calculated. This was achieved using the following data from Perry (1999):
Component Heat of formation
(kJ mol-1) Component Heat of solution
(kJ mol-1)
NaCl -407.48 CaCl2 20.52
CaCl2 -798.00 NaHCO3 -17.17
H20 -286.03 Na2CO3 23.32
NaHCO3 -929.89 NaCl -4.87
Na2CO3 -1151.91
CO2 -385.40
CaCO3 -1212.08
Table 8: Heat of formation and heat of solution for relevant components in RV1
The heat of reaction for the reactor RV1 was calculated using the heats of formation and the chemical equations (1) and (2):
The same procedure was carried out for reaction (2) which was found to have a heat of reaction of -77.13 kJ mol(CaCl2)-1. These values were converted to kJ kg-1 using the molecular mass of the relevant component and subsequently a heat duty (kJ h-1) by multiplying by the mass flow rate of the key component:
The heat duty reaction (2) was found to be -243 kJ h-1. When combining the heat duty values obtained for the reactor with respect to the heat of reactions, the overall heat duty was found to be 116 kJ h-1.
The heat of solution for the relevant components was converted to kJ kg-1 using the molecular mass and converted to a heat duty by multiplying by the mass flow rate of the component in the reactor. The example below is shown for NaCl:
The sum of all heat of solution heat loads was taken and found to be -692.9 kJ h-1.
As a result of all the data collected and calculated the overall energy balance for reactor RV1 was found. The amount of heat required to be supplied to the reactor in the heating coils was calculated using the following equation:
The required heat supply amounts to approximately 11 kW of energy from the heating coils.
References
Perry, R.H. and Green, D.W. (1999) ‘Physical and Chemical Data’, Perry’s Chemical Engineers’ Handbook. 8th edn. New York; London: McGraw-Hill, pp 2-1 - 2-516.
