K. Laturkar, Facility for Rare Isotope Beams, East Lansing, Michigan; and K. LATURKAR, Validation Associates LLC, Framingham, Massachusetts
Sensitivity analyses evaluate the effects of changes in certain variables on project simulations or investment economics.1 The analysis involves an automated procedure for adjusting input parameters of a stream or unit operation over a range of values and recording the results so that reliable and efficient operation can be achieved. This variation in parameters can facilitate design simulations in several ways, including:
Many operations in the process industries rely heavily upon shell-and-tube heat exchangers. Heat is transferred between two fluids that have different temperatures through the shell and tubes of these devices, and their efficiency is determined by the flow conditions of both fluids.
This article presents a sensitivity analysis of a typical shell-and-tube heat exchanger operation and utilizes DWSIM, an open-source simulation software,2 to determine how varying the inlet parameters impacts outlet parameters such as temperature, enthalpy, the overall heat transfer coefficient and the heat duty. The dependent variables are determined by the incremental variation of these inlet parameters over a specified range.3 Plotting the data allows for further assessment. It is important to note that sensitivity analysis in multiple case testing yields valuable information, but it may not provide a comprehensive analysis of how the processes should be conducted according to their design requirements, operational specifications or economic considerations.
Theory. The heat transfer across the surface of a heat exchanger4 is given by Eq. 1:
Q = U A ∆ Tm (Eq. 1)
For a heat exchanger, the individual resistances depend on the process type, fluid properties, flowrates and arrangement within the heat exchanger. By adding the reciprocals of these individual resistances, it is possible to calculate the overall heat transfer coefficient using Eq. 2:
For a heat exchanger with counter-current flow, the log mean temperature difference (LMTD) is given by Eq. 3:
Multiplying the LMTD with a correction factor yields the mean temperature difference. In addition to the fluid temperatures of the shell and tube, this correction factor is dependent on the number of shell-and-tube passes (Eq. 4):
∆Tm = Ft ∆Tlm (Eq. 4)
For a square pitch tube arrangement inside the heat exchanger, the equivalent diameter is given by Eq. 5 and will be required for the shell-side pressure drop calculation:
In flowing through the tube arrangement inside the heat exchanger, the fluid experiences reversals in flow along with sudden contraction and expansion and friction losses. The tube-side pressure drop—which accounts for that—is given by Eq. 6:
For the flow of the fluid on the shell side, there is axial as well as cross flow of the fluid due to the baffles installed in the shell of the heat exchanger. The shell-side pressure drop is given by Eq. 7:
Example. A counter-current, two-shell and eight-tube pass heat exchanger is considered with water and methanol flowing on the tube and shell side, respectively.5 On the tube side, water enters at 15,000 kg/hr at a temperature of 10°C and 1 bar. On the shell side, methanol enters the heat exchanger at 25,000 kg/hr at a temperature of 80°C and 5 bar.
Tube-side specifications. Tubes are considered to have an outer diameter of 20 mm, a thickness of 2.5 mm and are 5 m long. The number of tubes per shell is 1,024, with tube spacing of 25 mm in a square layout. The thermal conductivity is 60 W/mK while the tube roughness and fouling factor are 0.05 mm and 0.00035 Km2/W, respectively.
Shell-side specifications. The shell diameter is taken as 1,000 mm, with a typical baffle spacing of 250 mm and a 25% baffle cut based on the total number of tubes in the bundle. The fouling factor on the shell side is also 0.00035 Km2/W.
Results and discussions. A simulation of this heat exchanger was performed on DWSIM. Using Raoult's law thermodynamic package and nested loops for the flash algorithm, the flowsheet was simulated based on the values given in the problem statement.
After the heat exchange, the water outlet temperature increased to 66.16°C while the methanol cooled to 40.97°C with only a minor decrease in the pressure drop on both sides of the shell-and-tube heat exchanger. The total calculated heat exchange area was 319.125 m2 with a global heat transfer coefficient of 191.78 W/[m2.K] and a heat load of 968.746 kW. The LMTD calculated from the outlet temperatures is 21.262°C with a thermal efficiency of 79.06%.
SENSITIVITY ANALYSIS APPROACH
The sensitivity analysis was carried out to see the effects of change in inlet water flowrate at various temperatures on the different parameters defining the heat exchanger. The study evaluated the effects on methanol outlet temperature, methanol outlet molar enthalpy, heat load on the exchanger, and maximum theoretical heat exchange possible for the configuration.
Case 1: Variation of methanol outlet temperature with inlet water mass flowrate at different temperatures. The methanol (outlet) temperature is shown in FIG. 1 as a function of water (inlet) flowrate, which is varied between 5,000 kg/hr and 25,000 kg/hr at a constant methanol inlet flowrate and temperature of 25,000 kg/hr and 80°C, respectively. There are five curves, each representing inlet water temperature at 5°C, 10°C, 15°C, 20°C and 25°C. As the flowrate of inlet water increases, the temperature of the methanol that exits the exchanger decreases.
Further, the temperature attained by methanol at a particular flowrate differs, depending on the water inlet temperature. The specific heat rate climbs with an increase in the inlet water mass flowrate, which in turn increases the heat transfer. As a result, the methanol outlet temperature decreases. It is observed that the temperature of the methanol outlet increases as the temperature of the cold water inlet increases. A temperature difference determines the rate of heat transfer, so a higher inlet water temperature results in a smaller temperature difference, resulting in a lower heat transfer rate.
Case 2: Variation of methanol outlet molar enthalpy with inlet water mass flowrate at different temperatures. In FIG. 2, the molar enthalpy (outlet) of methanol as a function of water (inlet) flowrate is depicted at a constant methanol inlet flowrate and temperature of 25,000 kg/hr and 80°C, respectively. The inlet water temperature is indicated by five curves at 5°C, 10°C, 15°C, 20°C and 25°C. As can be seen from the curves, at a given temperature, the methanol outlet enthalpy decreases as the inlet water flowrate increases. The enthalpy of a substance is a function of its heat capacity and temperature, according to thermodynamic laws. In this case, as the heat capacity is constant, the enthalpy increases with increasing temperature, suggesting that the enthalpy directly scales with temperature as substantiated by the curves.
Case 3: Variation in heat load for the heat exchanger with inlet water mass flowrate at different temperatures. At a constant methanol inlet flowrate of 25,000 kg/hr and an outlet temperature of 80°C, FIG. 3 illustrates the heat load for the heat exchanger as a function of water flowrate (inlet). Five curves demonstrate the inlet water temperature at 5°C, 10°C, 15°C, 20°C and 25°C. Since the heat load is directly proportional to the mass flowrate of the flowing medium, the heat load of the exchanger increases as the mass flowrate of the water increases. Also, the heat load is directly proportional to the temperature difference between the two sides of the exchanger. The greater the difference, the higher the heat load, which is validated by the curves.
Case 4: Variation of maximum theoretical heat exchange with inlet water mass flowrate at different temperatures. Based on a constant methanol inlet flowrate and temperature of 25,000 kg/hr and 80°C, respectively, FIG. 4 shows the variation in maximum theoretical heat exchange possible with the inlet water mass flowrate for the given heat exchanger. A range of five curves indicates the temperature of the inlet water at 5°C, 10°C, 15°C, 20°C and 25°C. Under ideal conditions, assuming no heat or frictional losses to the surrounding environment, the maximum theoretical heat exchange reaches a maximum and then remains constant regardless of the increase in mass flowrate. It is here that the heat exchanger is limited by only the geometry of the heat exchanger surface, not the flowrate of the transferring medium. Another factor affecting the heat exchanger here is the temperature differential. By interpreting the curves, it is evident that the greater the difference, the greater the theoretical heat exchange.
Takeaway. The case study presented here has used sensitivity analysis to examine various "what if" scenarios associated with alternative outlining assumptions. By carrying out a detailed and exhaustive theoretical study, it is possible to set up various parameters to evaluate the results and determine the optimum exchanger operating points. This proactive approach can lead to both cost savings, and the detection and avoidance of potential complications during operations. HP
ACKNOWLEDGEMENT
This article was inspired by a chapter written by S. M. Wagh, D. P. Barai and M. H. Talwekar on ChemCAD's ability to perform sensitivity studies on shell-and-tube heat exchangers6 and it interested the authors to investigate if the open-source software, DWSIM, could execute a similar comprehensive analysis.
GLOSSARY
Q Heat transferred/time
U Overall heat transfer coefficient
Uo Overall heat transfer coefficient based on the outside area of the tube
A Area of heat transfer
∆Tm Mean temperature difference
ho Outside fluid film coefficient
hi Inside fluid film coefficient
hod Outside dirt coefficient
hid Inside dirt coefficient
kw Thermal conductivity
di Inside tube diameter
do Outside tube diameter
Nt Number of tubes
T1 Inlet hot fluid temperature
T2 Outlet hot fluid temperature
t1 Inlet cold fluid temperature
t2 Outlet cold fluid temperature
∆Tlm Log mean temperature difference (LMTD)
Ft Temperature correction factor
∆Pt Tube-side pressure drop
Np Number of tube passes
L Length of tube
µ Fluid viscosity at the bulk fluid temperature
µw Fluid viscosity at the wall
jf Dimensionless friction factor
ρ Density of the fluid
ut Fluid velocity in the tube
uS Fluid velocity in the shell
∆PS Shell-side pressure drop
lB Baffle spacing
DS Inside diameter of the shell
de Equivalent diameter
pt Tube pitch
LITERATURE CITED
KAUSTUBH LATURKAR is an Engineer at the Facility for Rare Isotope Beams, Michigan State University, which is a U.S. Department of Energy project in Michigan, U.S. He has more than 8 yr of experience in the fields of process engineering, refinery operations, utility systems design and operation, with a special focus on the design and commissioning of engineering systems. He earned an MS degree in chemical engineering from the University of Florida and a BE degree in chemical engineering from Panjab University, Chandigarh, India.
KASTURI LATURKAR works as a Validation Engineer for Validation Associates LLC. She graduated with an MS degree in chemical engineering from Syracuse University and a B.Tech degree in chemical engineering from Guru Gobind Singh Indraprastha University, Delhi, India. She has more than 3 yr of experience working in commissioning, qualification and validation of upstream and downstream bioprocessing equipment and critical utilities.