6.1.3.1.3 Equation Involved in Packed Bed Reactor Design 6.1.3.1.3.1 Rate law
Assumption:
1. The reaction is first order reaction.
2. The gas reactant and product obey ideal gas law.
3. Partial pressure of the reactant is calculated according to inlet pressure.
4. The reactor is assumed to be isothermal.
5. 80% of reactor is filled by catalyst.
Rate Law:
For reaction with pressure drop:
(
1)
From ideal gas law
Gly Gly
P =C RT
Since it is assumed that the reactor is isothermal, T=To
(
1)
Chapter 6: Packed Bed Reactor 1 Acrylic Acid Project
mol Gly 1 19 248000
(
1)
1.00 10
kg catalyst s 1 0.0698
RT Glyo o
The design equation for packed-bed reactor is given as:
Glyo Gly
6.1.3.1.3.3 Ergun equation for pressure drop
The gas-phase reaction is catalyzed by passing the reactant through a packed bed of catalyst particles. The equation used most to calculate pressure drop in a packed bed is the Ergun equation.
From Ergun equation, differential pressure drop across the tube is given as:
( )
Where z = length down the packed bed of tubeAt the entrance to the reactor:
Substitute (4) into (3):
Chapter 6: Packed Bed Reactor 1 Acrylic Acid Project Weight of catalyst, W = Volume of solid catalyst x Density of catalyst
Weight of catalyst, W = Volume of reactor x (1 – bed porosity) x Density of catalyst W = −
(
1 φ)
A zc ×ρc=ρbA zc6.1.3.1.3.4 Simultaneous Ordinary Differential Equations
The conversion and pressure profiles for the packed-bed reactor are governed by 2 ODEs:
1) 1 19 248000
(
1)
Since the reactor is assumed to be isothermal, Z=1.
The ODEs are solved simultaneously by substituting all the relevant values, with the aid of MATLAB 7.0.
Chapter 6: Packed Bed Reactor 1 Acrylic Acid Project 6.1.3.1.4 Packed Bed Reactor Optimization
The reactor size and performances are analyzed by using different parameters such as pressure, temperature and the reactor shell diameter.
The analysis is done by computing the variables with different pressure, temperature and flow area into the simultaneous equation. The result of weight of catalyst and the pressure ratio when the conversion, X=0.983[1] are obtained by solving the simultaneous equations using MATLAB software. The ratio of length and diameter of the reactor of different parameter are calculated.
The reactor size and performance are optimized based on the following criteria:
(i) The ratio of length to diameter of the reactor (L/D) must be within the range of 5-10.[5]
(ii) The pressure drop must be kept as low as possible or pressure ratio, Y as high as possible to prevent loss in pressure energy.
(iii) The amount of catalyst should not be extremely high due to the economic consideration.
Example of the result of MATLAB by using P = 1 bar and T = 275oC.
The result is shown in the plot obtained from MATLAB:
Figure 6.3: Plot of Conversion and Pressure Ratio Obtained from Matlab
Legend: Blue = Conversion Green = Pressure Ratio The accurate result is obtained from the “workplace” of MATLAB:
Chapter 6: Packed Bed Reactor 1 Acrylic Acid Project
Figure 6.4: Data of Conversion and Pressure Ratio Obtained from Matlab
6.1.3.1.4.1 Shell Diameter Analysis Assume
Pressure, P = 1.5 bar Temperature, T = 275oC
The number of tubes that can be placed in the reactor is depends on the size of the shell of the reactor. Hence an analysis is done to study the performance of the reactor by using different size of shell.
From the result of MATLAB, the weight of catalyst, W, pressure ratio, Y and the ratio of length and diameter of reactor, L/D are obtained and plotted against number of tubes.
Chapter 6: Packed Bed Reactor 1 Acrylic Acid Project
Table 6.4: Weight of Catalyst, W, Pressure Ratio, Y, Length of Reactor, L and Ratio of Length to Diameter, L/D at Different Number of Tube per Reactor [3]
Shell
Ratio of Length to Diameter, L/D
0.8 means reactor is 80% filled by catalyst
From Table 4, it shows that the dimensions of reactor with shell diameter = 1.4 m and number of tube per reactor = 733 gives the result of length to diameter ratio = 8.6238 which is in the range of design criteria (5-10). Hence it is the most suitable dimension of the reactor to optimize the process.
Chapter 6: Packed Bed Reactor 1 Acrylic Acid Project From reference [1], the optimum pressure lies between 1 bar to 2 bar.
From the result of MATLAB, the weight of catalyst, W, pressure ratio, Y and the ratio of length and diameter of reactor, L/D are obtained and plotted against inlet pressure.
Table 6.5: Weight of Catalyst, W, Pressure Ratio, Y, Length of Reactor, L and Ratio of Length to Diameter, L/D at Different Inlet Pressure, Po
Inlet Pressure, Po (bar)
Weight of Catalyst, W (kg)
Pressure Ratio, Y
Length of Reactor, L (m)
Ratio of Length to Diameter, L/D
1 2210 0.932 7.92 5.6552
1.1 2440 0.938 8.74 6.2438
1.2 2610 0.944 9.35 6.6788
1.3 2850 0.948 10.21 7.2929
1.4 3120 0.951 11.18 7.9838
1.5 3370 0.955 12.07 8.6235
1.6 3700 0.958 13.26 9.4680
1.7 3800 0.961 13.61 9.7239
1.8 3880 0.963 13.90 9.9286
1.9 3970 0.965 14.22 10.1589
2 4050 0.967 14.51 10.3636
Chapter 6: Packed Bed Reactor 1 Acrylic Acid Project From Table 5, the length to diameter ratio at pressure 1 to 1.8 bars is within the design range, 5-10. However, operating under low pressure might causes the pressure driving force not sufficient to drive the reactant along the reactor. The situation become worse if there is clogging fouling that causing the pressure drop across reactor higher than expected. The outlet pressure might drop to less than 1 atm, which is vacuum condition under these situations. Hence it is better to have a safety margin to operate at higher pressure. Pressure of 1.4 bar is selected as the catalyst used is not too high and L/D ratio is still within 5-10.
6.1.3.1.4.3 Temperature Analysis Set:
Shell inner diameter = 1.4 m Number of tube per reactor, n = 733 Pressure, P = 1.4 bar
From reference [1], the optimum pressure lies between 260oC to 280oC.
From the result of MATLAB, the weight of catalyst, W, pressure ratio, Y and the ratio of length and diameter of reactor, L/D are obtained and plotted against inlet temperature.
Chapter 6: Packed Bed Reactor 1 Acrylic Acid Project
Table 6.6: Weight of Catalyst, W, Pressure Ratio, Y, Length of Reactor, L and Ratio of Length to Diameter, L/D at Different Inlet Temperature, To
Inlet Temperature,
Ratio of Length to Diameter, L/D
From the Table 6, it is clearly show that 275oC is the best temperature to be operated because at 275oC, the ratio of length to diameter of reactor is 7.9838 which is in the range of design consideration, which is 5-10.
6.1.3.1.4.4 Result of Packed Bed Reactor Optimization Analysis
Table 6.7: Results of Packed Bed Reactor Optimization Analysis
Parameter Value Inlet Pressure, Po (bar) 1.4
Inlet Temperature, To (oC) 275 Number of Tubes per Reactor, n 733 Total Number of Tubes, N 1466 Shell Diameter, IDs (m) 1.4 Weight of Catalyst, W (kg) 3120 Pressure Ratio, Y 0.951 Outlet Pressure, P=YPo 1.3314 Length of Reactor, L (m) 11.18 Ratio of Length to Diameter, L/D 7.9838