Production of Heptenes from Propylene and Butenes
Group 12
Leader guy: Steve Wood
Union Workers:
Matt Huelsman
Patrick Luck
December 11, 1998
Abstract
The purpose of this project was to optimize heat exchange in the production of heptene from propylene and butenes. The base case heat exchange system included five equivalent exchangers used to cool the reactor, four exchangers used to heat and cool process streams, and reboilers and condensers on three distillation columns. We determined that the most important consideration in a feasible economic optimization was reducing the duty of the first process stream exchanger, which used low-pressure steam to heat and vaporize the reactor effluent. Exchanging heat between the three uncooled product streams and the reactor effluent decreased the amount of low-pressure steam needed, and also reduced the cost of cooling the product streams. In addition, using each of the cooled product streams from a single exchange to further heat the reactor effluent by incorporating additional exchangers earlier in the process was found to decrease the overall cost. It was determined that using this process over 20 years would save $631,000 in utilities over the base case. However, because the product streams would be used to heat up the initial stream, additional exchangers would be needed. This would increase the capital cost by $100,000, giving an estimated overall savings of $531,000 for a plant life of 20 years.
Table of Contents
The main products that result from the reaction of propylene and butenes are 1-hexene, 1-heptene, 1-octene, and 1-undecene. There are also several minor side reactions. The reactor effluent is separated into C3, C4, hexenes, heptenes, and C8 + heavies. The actual base case consists of a reactor equivalent to five CSTAR reactors in series, each with its own cooling water heat exchanger. Next, there is a 20-stage distillation column that separates the C3 and C4 from the heavier products. After this is a 38-stage distillation column that separates hexenes from the hydrocarbon stream. Finally, a 41-stage distillation column separates heptenes as top products from C8 + heavies. Throughout this process are 16 heat exchangers. These include three reboilers, three condensers, three product coolers, one heater and five coolers for the reactor.
The base case was appraised exactly as printed in the book. The overall cost for the exchangers was found to be $3,230,000 when priced over 20 years at a 7% discount rate. In addition, it was decided for reasons that will be explained later to also price the base case using stainless steel instead of the carbon steel employed in the book. The price for this base case was $3,540,000, an increase of $310,000 over the book base case. Chart 1 shows the breakdown in overall cost among the exchangers.
Chart 1
Almost all of the cost from heat exchange can be attributed to the three reboilers (E-503, E-505, E-508) and the exchanger that uses low pressure steam to heat and vaporize the reactor effluent (E-502). Therefore, these are the most important considerations in heat integration.
For computer simulation of the heat exchange system, HYSYS was chosen because of its ability to handle hydrocarbon streams. The HYSYS Reference Manual suggests use of the Peng-Robinson property package for "rigorous treatment of hydrocarbon systems" (p. 342). The Lee-Kesler equation of state was chosen as the enthalpy method specification because according to the HYSYS user guide, "The Lee-Kesler enthalpies may be slightly more accurate for heavy hydrocarbon systems" (p. 351).
Below is a summary of streams in the base process and their temperatures. The italicized streams are those which need to be cooled, and the bold streams are those which need to be heated.
|
Stream |
Temperature ( ° C) |
Stream |
Temperature( ° C) |
|
1 |
25 |
11 |
135 |
|
2 |
25 |
12 |
107 |
|
3 |
26 |
13 |
107 |
|
4 |
45 |
14 |
154 |
|
5 |
45 |
Column 1 Reboiler |
151 |
|
6 |
45 |
Column 2 Reboiler |
135 |
|
7 |
45 |
Column 3 Reboiler |
154 |
|
8 |
151 |
Column 1 Condenser |
55 |
|
9 |
78 |
Column 2 Condenser |
78 |
|
10 |
78 |
Column 3 Condenser |
107 |
Only stream fourteen is hot enough to transfer duty to any of the reboilers, but this would be economically inefficient because of the small temperature difference and because stream 14 can be used to heat stream 4 which allows a much greater average temperature difference in the exchanger.
The following chart shows the heat intervals for the four remaining streams: stream 4, Column 2 Condenser, Column 3 Condenser, and Column 3 Reboiler.
Stream four requires more duty than can be provided by streams 10, 13, and 14 combined. In order to transfer more heat, the vapor distillate from column T-502 and T-503 were split into reflux and product streams before they were condensed, thereby transferring the latent heat from the product streams directly to stream four. The heat intervals for this set-up are shown below.
This reduced both heating costs for stream four and cooling costs for the product streams. The reflux streams were sent through condensers in order to prevent process control problems caused by transferring the latent heat of the reflux streams to stream 4, which is much earlier in the process.
The above cascade diagram, for the case in which the vapor product streams were used to heat the reactor effluent (stream 4), shows that the pinch temperature for our system is 73 C, which is consistent with how we optimized the system based on the temperature interval diagrams. This cascade diagram also shows how much duty will be required in exchangers transferring heat by means of low pressure steam or cooling water.
4.1 Exchanger Material of Construction
The winning group for the optimized heptene reactor reported: "The original design suggested the use of carbon steel heat exchange tubes for use in cooling water duty. While there is not much temperature stress on that system (the cooling water varies between 35 and 45
° C), it was suggested by Dr. C. A. Armeniades of Rice University, that we use stainless steel tubes instead. Corrosive effects were predicted due to the use of water and conditions indicated that scaling would likely occur if CS was used. Dr. Armeniades advised that cost savings would be created in long term analysis of the system, as the CS tubes would require more maintenance and more frequent replacement/overhaul work if used in cooling water service." In fact, it is a good idea to use stainless steel for every heat exchanger in the process, because:4.2 Tube-Side and Shell-Side Streams
The textbook suggests the tubes for "corrosive, fouling, scaling, and high pressure fluids," and the shell for "viscous and condensing fluids." Although the hydrocarbons are more fouling than water and water is more viscous than the hydrocarbon streams, the potential corrosive effects of water is a more important consideration. The low-pressure steam was used in the shell of E-502, the exchanger that heats the reactor effluent, upon the suggestion by Kern that the steam be put on the shell side to localize corrosion (p. 193). Exchangers E-507 and E-511, which cool the product streams with water, have the cooling water stream on the tube-side because of the significantly increased turbulence with this configuration. Where a hydrocarbon stream heats another hydrocarbon stream, if one stream is vaporized it is in the tubes; if one stream condenses, it is on the shell side. Otherwise, the choice was made on the basis of turbulence (the Reynolds numbers were kept as high as possible, and by switching the tube-side and shell-side streams, the lower Reynolds number could be increased in some cases).
For exchangers in which there was only liquid flow, and the required exchange area was less than 10 m2, a double pipe exchanger was used upon suggestion of both our textbook and Kern. For exchangers in which there was only liquid flow, and the required exchange area was more than 10 m2, a multiple pipe exchanger was used. For condensers, fixed tube sheet exchangers were chosen because they are conventionally used for condensers. For other exchangers in which there was both liquid and vapor flow, a pull-through floating head exchanger was used to eliminate the problem of differential expansion, thereby reducing the likelihood of applying too much stress on the stationary tube sheets (Kern, p. 132). Other types of exchangers were considered, but were more costly than those eventually chosen. The fact that turbulent flow existed in the shell- and tube-sides of all exchangers meant that heat exchange was significant, and the relatively small number of tubes in each exchanger allowed multiple-pipe exchangers to be used without the need of a tube-sheet exchanger (p.131). Fancier styles of heat exchangers were not needed.
4.4 Number of Passes in Exchanger
Upon initial estimation, the number of shell passes was taken to be equal to the number of tube passes for each exchanger. This eliminates the problem of co-current flow in part of the exchanger that results from the use of a 1-2 or 2-4 exchanger. A counter-current/co-current exchanger comes in handy if the velocity of fluid either on the shell side or the tube side is too low, or if the size of the exchanger would cause it to collapse as a result of using multiple steel plates to maintain counter-current flow. We did not experience this problem in our exchangers, and therefore maintained use of cross-current floating head exchangers and cross-current flow in the double and multiple pipe exchangers. When the calculated length of an exchanger exceeded 20 feet, additional passes were added until the length of an individual hairpin did not exceed 20 feet, and heuristic suggested by Kern (p. 103).
Triangular pitch always provides better overall heat exchange than square pitch (approximately 25% better, according to Kern on p. 136), but triangular tube bundles are very hard to clean. Because of the high dirt / fouling factor associated with hydrocarbon streams, it may be desired to clean the tube bundles often. We opted for square pitch, which costs more in the initial analysis, but saves a lot of time and money in the long run.
Baffles are used on the shell-side of a heat exchanger to promote turbulent flow, and as a way of supporting the tubes in the exchanger. Kern states that baffles should never be placed at a greater spacing than the inner diameter of the shell, and never closer than a distance one-fifth the inner diameter of the shell (p. 129). In cases where the Reynolds number of the shell-side stream exceeded 10,000, baffles were spaced at a distance equal to the inner diameter of the shell. When the Reynolds number of the shell-side stream was between 2000 and 5000, the baffles were spaced at a distance equal to one-fifth the inner diameter of the shell. And when the shell-side Reynolds number was between 5000 and 10,000, the baffles were spaced a distance equal to one-third the inner diameter of the shell. This spacing arrangement is conservative, and should provide turbulent flow even in cases where the shell-side flow is unexpectedly low.
We opted for the segmented baffle (Figure 7.6 in Kern), which is by far the most commonly used type of baffle, and therefore should be easily replaceable.
Kern specifies many possible tube-sheet layouts for square pitch multi-tube exchangers and floating-head exchangers. Of these the optimal was chosen as the one which provided highly turbulent flow while minimizing pressure drop through the exchanger. Sometimes a trade-off had to be made in which case the turbulence of the streams was more important because it ensures high overall heat-transfer coefficients. Kern's specifications provided standard tube ID and OD wall-thickness and shell ID for a given number of tubes passes (p.841).
Kern also states the most common double-pipe exchanger dimensions (p. 110). Turbulence was again the most important factor, and when this was not a problem, the pressure drop over the tube was minimized.
The tube and pipe wall thickness was of little concern because of the low operating pressure. BWG 18 tubes were chosen which have wall thickness of .049 inch wall thickness and standard schedule 40 (pp. 843-844) was chosen for the pipes.
4.8 Pressure Drop Through Exchanger
Kern gives a detailed method for calculating the pressure drop over an individual heat exchanger. Refer to Appendix 1 for this calculation, and Appendix 2 for sample calculations. A spreadsheet showing all calculated pressure drops is given in Appendix 3 (note: the unchanged exchangers were included only to calculate number of passes and number of baffles, not to determine pressure drop).
4.9 Overall Heat Transfer Coefficient in Exchanger
Kern gives a method for approximating the overall heat transfer coefficient in an exchanger. Again, a detailed explanation of this method is given in Appendix 1 and sample calculations are given in Appendix 2. A spreadsheet including all calculated heat transfer coefficients is given in Appendix 3.
5.1 Further Optimization of Exchanger Arrangement
The initial optimization which used streams 10, 13, and 14 saved approximately $500,000 over the cost of the base case over twenty years discounted at 7% annually (see Appendices 6 and 7 for complete calculations). However, after this was done, it was found that significant additional savings could be obtained by reusing 10, 13, and 14 to heat stream 4 earlier in the process. This is shown in the following diagram.
When deciding whether to use this further optimization, it must be determined whether these nine exchangers can be proximally arranged to fit into a plant without excessive use of pipes, and without sacrificing safety or access to the exchangers in the process. We found many examples on the Internet of enormous heat exchangers used in industry, the dimensions of which dwarf those of our exchanger system (given in the table below). Our conclusion is that a spatial arrangement can be easily found in which these exchangers transfer process streams, low pressure steam, and cooling water without the need of extensive piping systems, while leaving plenty of room for easy access to the exchangers.
We initially used 5 C as the minimum approach temperature for all exchangers, and we optimized the system of exchangers using this approach; we then optimized the individual exchangers in the optimized system, changing the minimum approach temperatures of the exchangers to correspond to minimum overall cost over 20 years. This saved approximately $10,000, but more importantly gave more desirable heat-exchanger dimensions.
The tables below show selected parameters of every stream and exchanger in the optimized system (a more detailed spreadsheet is given in Appendix 4).
Streams in optimized case
|
Stream |
Pressure (kPa) |
Temperature ( ° C) |
Stream |
Pressure (kpa) |
Temperature ( ° C) |
|
4 |
770 |
45 |
14 cooled |
200 |
81.60 |
|
4b |
767.8 |
47.94 |
Recycle 10 cooled |
200 |
47 |
|
4c |
765.5 |
56.60 |
Recycle 13 cooled |
150 |
49.94 |
|
4d |
717.8 |
59.01 |
Recycle 14 cooled |
199.9 |
57.1 |
|
4e |
715.1 |
74.84 |
511 cw in |
401.3 |
30 |
|
4f |
710.6 |
81.10 |
511 cw out |
401.1 |
40 |
|
4g |
703.2 |
82.81 |
507 cw in |
401.3 |
30 |
|
Into column 501 |
701.6 |
103 |
507 cw out |
401.3 |
40 |
|
10 |
200 |
90.45 |
14 out |
199.8 |
45 |
|
13 |
150 |
109.6 |
13 out |
150 |
45 |
|
14 |
200 |
154 |
E-502 lps in |
601.3 |
160 |
|
10 cooled |
200 |
67.01 |
E-502 lps out |
601.3 |
158 |
|
13 cooled |
150 |
92.84 |
|||
Heat exchangers in optimized case
|
Exchanger |
Duty (MJ/hr) |
exchange area (m2) |
Type of exchanger |
# of baffles |
# of pipes |
# of passes |
Tube ID (in) |
Tube OD (in) |
Shell ID (ft) |
Bare module cost ($) |
|
E-100 |
688.8 |
27.20 |
Float head |
18 |
16 |
1 |
1.15 |
1.25 |
0.833 |
45,964 |
|
E-101 |
896.1 |
16.71 |
Float head |
5 |
16 |
1 |
1.15 |
1.25 |
0.833 |
37,258 |
|
E-102 |
237.7 |
7.80 |
Float head |
10 |
16 |
1 |
1.15 |
1.25 |
0.833 |
30,586 |
|
E-103 |
73.1 |
6.15 |
Double pipe |
154 |
1 |
3 |
3.068 |
3.5 |
0.336 |
5,147 |
|
E-104 |
261.4 |
12.41 |
Multiple pipe |
12 |
16 |
1 |
1.15 |
1.25 |
0.833 |
6,467 |
|
E-105 |
87.7 |
7.12 |
Multiple pipe |
6 |
16 |
1 |
1.15 |
1.25 |
0.833 |
5,248 |
|
E-502 |
1764.0 |
11.58 |
Float head |
12 |
32 |
1 |
0.652 |
0.75 |
0.667 |
32,274 |
|
E-507 |
29.0 |
1.40 |
Double pipe |
96 |
1 |
2 |
2.067 |
2.38 |
0.256 |
4,710 |
|
E-511 |
35.0 |
0.96 |
Double pipe |
98 |
1 |
1 |
1.38 |
1.66 |
0.172 |
4,601 |
|
E-506 |
1990.0 |
15.14 |
Tube Sheet |
25 |
16 |
1 |
1.15 |
1.25 |
0.833 |
27,619 |
|
E-509 |
1350.0 |
6.11 |
Tube Sheet |
10 |
16 |
1 |
1.15 |
1.25 |
0.833 |
18,774 |
|
E-501A-E |
846.0 |
61.40 |
Tube Sheet |
95 |
16 |
1 |
1.15 |
1.25 |
0.833 |
146,715 |
|
E-503 |
1251.0 |
32.10 |
Float head |
10 |
16 |
1 |
1.15 |
1.25 |
0.833 |
25,994 |
|
E-505 |
2184.0 |
21.10 |
Float head |
7 |
16 |
1 |
1.15 |
1.25 |
0.833 |
21,552 |
|
E-508 |
2026.0 |
75.30 |
Float head |
23 |
16 |
1 |
1.15 |
1.25 |
0.833 |
40,137 |
|
E-504 |
3577.0 |
128.50 |
Tube Sheet |
200 |
16 |
2 |
1.15 |
1.25 |
0.833 |
45,002 |
Referring to the graph below, the increase in capital cost from the base case to the optimized case comes from the increased number of exchangers that are included in the optimized case. However, there was a significant savings on utilities over 20 years; the base case utilities cost $2,892,000 compared to the optimized case utilities of $2,261,000. The total base case cost is $3,233,000 for carbon steel and $3,545,000 for stainless steel compared to the optimized cost of $3,013,000 over a 20 year period, for an overall savings of about $533,000 over the stainless steel case. However, the actual savings over the base case would be greater than this predicted value, because the base case as specified in the book estimates exchanger duties that are significantly lower than those predicted by HYSYS using the same stream specifications. For example, E-502 requires approximately 25% more low-pressure steam in a HYSYS simulation than as stated in the base case in the book, accounting for another $250,000 savings in the optimized case.
The change in utilities is almost exclusively from the change in low pressure steam provided to E-502. The capital cost for exchangers is exclusively from the new exchangers added to the system in order to provide double exchange for each product stream; still, the capital cost is a very minor consideration compared to the utility cost, as shown in the Breakdown and Comparison of Optimized Case graph below.
Breakdown and Comparison of Optimized Cost
Appendix 1: Equations used to determine overall heat transfer coefficient and pressure drop
Appendix 2: Sample calculations for overall heat exchange and pressure drop
Appendix 3: Excel files showing all calculated variables for heat transfer and pressure drop
Appendix 4: All stream specifications for optimized case
Appendix 5: Base case CapCost
Appendix 6: Optimized case CapCost
Appendix 7: Base-case, optimized case cost
Pressure drop calculations
The pressure drop of the shell-side fluid is
(7.44)
where
DPS is the shell-side pressure drop (psf)
f is a friction factor determined by Figure 29 (ft2/in2)
Gs is the shell-side mass velocity (lb/hr*ft2)
Ds is the inside diameter of the shell (ft)
N is the number of shell-side baffles
De is the equivalent diameter for pressure drop (ft) given by
(7.4)
s is the shell-side specific gravity
fs is the viscosity ratio, (m/mw)0.14, taken to be 1 for our calculations
m is the viscosity of the shell-side fluid (cp)
mw is the viscosity at the tube-wall temperature (cp)
PT is the tube pitch (in)
Nt is the number of tubes
d0 is the outside diameter of tubes (in)
The pressure drop of the tube-side fluid is given by
(7.47)
(7.45)
(7.46)
where
DPT is the total tube-side pressure drop (psf)
DPt is the single-tube pressure drop (psf)
DPr is the tube-side return loss (psi)
f is a friction factor determined by Figure 26 (ft2/in2)
Gt is the tube-side mass velocity (lb/hr*ft2)
L is the length of the tube (ft)
n is the number of tube passes
V is the velocity (ft/s)
G' is the acceleration of gravity (ft/s2)
s and ft are the tube-side equivalents to the shell-side s and ft
When there is a phase change, Kern gives the following as ways to approximate the pressure-drop and heat exchange behavior:
Overall heat transfer coefficient calculations
The heat transfer coefficient, UD, includes a fouling factor, which is .002 for "crude oil streams" up to 200 ° F (p. 846). Incorporating the fouling factor,
(6.10)
where Rd is the fouling factor and UC is the "clean coefficient." UC is related to side-specific heat transfer coefficients by
(6.6)
where hio is the heat transfer coefficient for the inside fluid referred to the pipe outside diameter, and ho is the transfer coefficient for the outside fluid. The variable hio is related to hi, the general heat transfer coefficient for the inside fluid, by
(6.5)
where ID and OD are the inner and outer diameter of the tubes, respectively. The value for ho is obtained from the equation,
(6.15b)
where De is the equivalent diameter for heat transfer (ft)
(6.3, 7.4)
k is the thermal conductivity of the transfer medium (p. 799 of Kern gives, for steel, k=26 Btu/hr*ft2*F/ft) , Gs is the mass velocity on the shell side, m is the viscosity of the fluid on the shell side, c is the specific heat of the shell-side fluid, and mw is the viscosity at the tube-wall temperature. An experimental curve (Figure 28) is used to determine the value of jH; (m/mw)0.14 was taken to be 1 for our calculations. Similarly, for the heat transfer coefficient of the inside fluid,
(6.15a)
where D is the inside diameter of tubes, and jH is determined from the experimental curves on Figure 24. The variables c, m, and mw are of the tube-side fluid.
Sample Calculations
Overall Heat Transfer Calculations for E-511 Heat Exchanger
Dirt factor, as stated in Table 12 on page 846 of Kern,
Rd=0.002
Thermal conductivity of steel, as given in Table 3 on page 799 of Kern,
k=26 Btu/hr*ft2*(° F/ft)
Equivalent diameter for pressure drop, as found in pressure drop calculations,
De=0.07625 ft
Inside tube diameter, as used in pressure drop calculations
D=1.38 ft
Mass velocity on shell side, as found in pressure drop calculations
Gs=336048.5899 lb/hr*ft2
Mass velocity on tube side, as found in pressure drop calculations
Gt=177710.7547 lb/hr*ft2
Shell-side viscosity, as used in pressure drop calculations
ms=0.95569 lb/hr*ft
Tube-side viscosity, as used in pressure drop calculations
mt=1.75222 lb/hr*ft
Shell-side Reynolds number for heat transfer
Res=( De*Gs ) / ms
=( 0.07625 ft * 336048.5899 lb/hr*ft2 ) / (0.95569 lb/hr*ft )
=26811.87
Tube-side Reynolds number for heat transfer
Re=( D*Gt ) / mt / ( 12 in/ft)
=( 1.38 ft * 177710.7547 lb/hr*ft2 ) / ( 1.75222 lb/hr*ft) / ( 12 in/ft)
=11663.35
Shell-side heat transfer value found from Figure 28 on page 838
jHs=92
Tube-side heat transfer value found from Figure 24 on page 834
jHt=40
Average molecular weight of shell-side fluid, as given by HYSYS
mws=120.56 g/mol
Average specific heat of shell-side fluid, as given by HYSYS
cs=( 75.3 kJ/kgmol*C ) / (mws) / 1000 * 453.5928 * .9486001 * (5/9)
=0.149303 Btu/lb*F
Average specific heat of tube-side fluid, as given by HYSYS
ct=277.58 kJ/kgmol*C
Heat transfer coefficient on outside of tubes
ho=(jHs*k/De)*(k/(cs*ms))-1/3
=(92*26/.07625 ft)*(26/(.149303 Btu/lb*F .95569 lb/hr*ft))-1/3
=5533.390593 Btu/hr*ft2*F
Heat transfer coefficient on inside of tubes
hi=(jHt*k/D)*(ct*mt/(k))1/3
=(40*26/1.38 ft)*(277.58 kJ/kgmol*C * 1.75222 lb/hr*ft /(26))1/3
=
2000.576968 Btu/hr*ft2*FInner diameter of tubes, as used in pressure drop calculations
ID=1.38 in
Outer diameter of tubes, as used in pressure drop calculations
OD=1.66 in
hi with respect to the tube OD
hio=hi*ID/OD
=( 2000.576968 Btu/hr*ft2*F ) * (1.38 in) / (1.66 in)
=1663.130251 Btu/hr*ft2*F
Clean overall heat transfer coefficient
UC=ho*hio/(ho+hio)
=(5533.4 Btu/hr*ft2*F)*(1663.1 Btu/hr*ft2*F )/(5533.4+1663.1Btu/hr*ft2*F)
=1278.777549 Btu/hr*ft2*F
From overall heat transfer calculations,
UD=UC/(UC*Rd+1)
=( 1278.777549 Btu/hr*ft2*F ) / ( 1278.777549 Btu/hr*ft2*F * .002 + 1)
=2265.989002 kJ/C*hr*m2
From HYSYS, using cross-current flow for Tlm:
U*A=2183.7 kJ/C*hr
Exchanger area:
A=(U*A)/UD
=(2183.7 kJ/C*hr)/( 2265.989002 kJ/C*hr*m2)
=0.963704199 m2
Pressure Drop Calculations for E-511 Heat Exchanger
Type of exchanger (preliminary guess)
Double Pipe
Inside diameter of tube (preliminary guess; option as given in Kern)
D=1.38 in
Inside diameter of shell (preliminary guess; option as given in Kern)
Ds=(2.067 in)/12
=0.17225 ft
Outside diameter of tube (preliminary guess; option as given in Kern)
d0=1.66 in
Equivalent diameter for heat transfer (option as given in Kern)
De=(.915 in)/12
=0.07625 ft
Equivalent diameter for pressure drop (option given in Kern)
De'=(.4 in)/12
=0.0333333 ft
Exchanger area, from UD calculations,
A=0.963704199 m2
Shell Density, from HYSYS,
rs=(rin+rout)/2
=(690.36 kg/m3 + 700.56 kg/m3)/2
=695.46 kg/m3
Tube Density, from HYSYS,
rt=(rin+rout)/2
=(1003.7 kg/m3 + 996.08 kg/m3)/2
=999.89 kg/m3
Shell viscosity, from HYSYS,
ms=(min+mout)/2
=(0.37121 cp + 0.41891 cp)/2
=(0.39506 cp) * (241.9085 (lb/hr*ft)/cp)
=0.95569 lb/hr*ft
Tube viscosity, from HYSYS,
mt=(min+mout)/2
= (0.79723 cp + 0.65143 cp)/2
=(0.72433 cp) * (241.9085 (lb/hr*ft)/cp)
=1.75222 lb/hr*ft
Shell mass flow, from HYSYS,
Fs=1261.1 kg/hr
Tube mass flow, from HYSYS,
Ft=837.27 kg/hr
Mass velocity on shell side
Gs=Fs*( 2.20462 lb/kg ) / ( p*(Ds/2)2 - p*(d0/12/2)2 )
=( 1261.1 kg/hr ) * (2.20462 lb/kg ) / ( p*(0.17225 ft /2)2 - p*(1.66 in/12/2)2 )
=336048.5899 lb/hr*ft2
Mass velocity on tube side
Gt=Ft*( 2.20462 lb/kg ) / ( p*(D/12/2)2 )
=( 837.27 kg/hr ) * (2.20462 lb/kg ) / ( p*(1.38 in/12/2)2 )
=177710.7547 lb/hr*ft2
Reynolds number for pressure drop on shell side
Res=( De'*Gs ) / ms
=( 0.0333333 ft * 336048.5899 lb/hr*ft2 ) / ( 0.95569 lb/hr*ft )
=11721.03666
Reynolds number for pressure drop on tube side
Ret=( De'*Gt ) / mt
=( 0.0333333 ft * 177710.7547 lb/hr*ft2 ) / (1.75222 lb/hr*ft )
=3380.681403
Shell-side friction factor, as found in Figure 29 on page 839 of Kern
fs=0.00205
Tube-side friction factor, as found in Figure 26 on page 836 of Kern
ft=0.000365
Specific gravity on shell side
ss=(rs) / (1000 kg/m3)
=(695.46 kg/m3) / (1000 kg/m3)
=0.69546
Specific gravity on shell side
st=(rt) / (1000 kg/m3)
=(999.89 kg/m3) / (1000 kg/m3)
=0.99989
Tube length
L=A * ( 3.28084 ft/m )2 / ( 2*p*(Ds/2) )
=( 0.963704199 m2 ) * ( 3.28084 ft/m )2 / ( 2*p*( 0.17225 ft /2) )
=19.16923363 ft
=> Number of tube passes, using maximum allowable single pass length of 20 ft as specified in Kern (p. 228), is 1.
Tube velocity
vt=( Ft/rt )*( 3.28084 ft/m )3 / ( 3600 s/hr ) / ( p*(D/2/12)2 )
=(837.27 kg/hr/ 999.89 kg/m3)*(3.28084 ft/m)3/(3600 s/hr)/(p*(1.38 in/2/12)2)
=0.79082501 ft/s
Pressure drop in shell
DPs=( fs*Gs2*L ) / ( 5.22´ 1010*De*ss)
=(.00205*(336049 lb/hr*ft2)2*19.16923363 ft)/(5.22´ 1010*0.07625 ft*.69546)
=( .011204443 psi ) * (6.894745 kPa/psi)
=0.077252 kPa
Return pressure drop in tube
D
Pr=4*vt2 / ( 2*st*g')=4*( 0.79082501 ft/s )2 / ( 2* 0.99989 * 32.22 ft/s2 )
=0.038849 psi
Pressure drop in tube
DPt=( ft*Gt2*L ) / ( 5.22´ 1010*De*st)
=(.000365*(177711 lb/hr*ft2)2*19.169234 ft)/(5.22´ 1010*0.07625 ft*.99989)
=( ( .055522 psf ) / (144 psi/psf) * DPr ) * (6.894745 kPa/psi)
=0.270514 kPa