PDC Design
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Design of a Packed Distillation Column for a
Unit Operations Laboratory
By Mr. Craig D. Mansfield, University of Florida, Chemical Engineering
Graduating Term:
Degrees Earned:
Fall 2011
Bachelor of Science in Chemical Engineering (Magna Cum Laude)
Bachelor of Science in Chemistry (Cum Laude)
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Abstract
The design for a new packed distillation column for consideration as a new experiment for the University Of Florida
Department Of Chemical Engineering Unit Operations Laboratory was created to demonstrate the separation of
water and isopropanol (i-Pr) and to evaluate a parallel applied multi-correlation approach to creating a high accuracy
process model based on correlations with known margins of error. The final design produced features a core
distillation unit, capable of batch, semi-batch, and continuous operation, and a surrounding recycle and waste
management system, which is not covered in this paper. The nominal core system configuration was continuous
operation with 20 mol% i-Pr, 10 mol% i-Pr, and 60 mol% i-Pr compositions and 10.4 USGPH, 6.6 USGPH, and 3.9
USGPH flow rates for the feed, bottoms, and distillate material streams, respectively. This configuration had a 6.65
inch tall HTU, requires 3.42 NTU, and a minimum required height of 1.89 ft. The final column design used a 6 ft high
packing of ¼ in. Raschig Rings and had a 23.1% nominal “average tray efficiency,” which was an expectedly low value
due to the presence of an azeotrope at 67 mol% i-Pr.
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Table of Contents
Abstract ............................................................................................................................................................................. 2
Purpose of the Design ....................................................................................................................................................... 4
Chemical System Definition .............................................................................................................................................. 4
Overview of Design Process .............................................................................................................................................. 4
Pedagogical Considerations .......................................................................................................................................... 4
Nominal Design Constraints and Initial Parameters ..................................................................................................... 4
Model Selection Criteria ............................................................................................................................................... 5
Selection of Thermodynamic Properties Models ............................................................................................................. 6
Vapor Phase Model ....................................................................................................................................................... 6
Liquid Phase Model ....................................................................................................................................................... 6
Mixing Rules .................................................................................................................................................................. 6
Van der Waals ........................................................................................................................................................... 6
Wong-Sandler ........................................................................................................................................................... 6
Evaluation of Thermodynamic Properties .................................................................................................................... 6
Selection of Transport Properties Models ........................................................................................................................ 8
Viscosity Model ............................................................................................................................................................. 8
Surface Tension Models ................................................................................................................................................ 9
Thermal Conductivity and Dielectric Coefficient Models ............................................................................................. 9
Diffusivity Models ......................................................................................................................................................... 9
Gilliland Correlation .................................................................................................................................................. 9
Wilke and Chang Correlation .................................................................................................................................... 9
Sitaraman et al. Correlation ...................................................................................................................................... 9
Leffler and Cullinan Correlation .............................................................................................................................. 10
Selection of Flooding Model ........................................................................................................................................... 10
Selection of Loading Model ............................................................................................................................................ 10
Determination of Power Requirements.......................................................................................................................... 11
Selection of Heat Transfer Models ................................................................................................................................. 12
Nusselt Model ............................................................................................................................................................. 12
Mostinski Model ......................................................................................................................................................... 12
Modified Thöme and Shakir Model ............................................................................................................................ 12
Combined Model Evaluation and Heat Exchanger Sizing ........................................................................................... 12
Initial Sizing of the Reboiler ............................................................................................................................................ 13
Selection of Mass Transfer Models ................................................................................................................................. 13
Onda et al. Correlations .............................................................................................................................................. 13
Mass Transfer Behavior and Column Sizing .................................................................................................................... 13
Translation from Interfacial to Overall Mass Transfer ................................................................................................ 13
Design Integral ............................................................................................................................................................ 14
Column Sizing and Calculated Mass Transfer Behavior .............................................................................................. 14
Final Selection of Column ........................................................................................................................................... 14
Sizing the Condenser....................................................................................................................................................... 14
Final Sizing of the Reboiler .............................................................................................................................................. 15
Assembling the Completed Model.................................................................................................................................. 15
Description of Nominal System Design and Behavior..................................................................................................... 15
Column and Packing Material ..................................................................................................................................... 15
Reboiler ....................................................................................................................................................................... 15
Condenser ................................................................................................................................................................... 15
Nominal Operation ..................................................................................................................................................... 15
Nominal Lab Session ................................................................................................................................................... 16
Concluding Remarks........................................................................................................................................................ 16
Acknowledgements......................................................................................................................................................... 16
References ...................................................................................................................................................................... 17
Appendix A: Static Description of the Nominal Core System Description ...................................................................... 18
Appendix B: Diagram of Core System ............................................................................................................................. 24
Appendix C: Reboiler Design Schematic ......................................................................................................................... 25
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Purpose of the Design
The author’s research was spurred by his mentor’s proposition of comparing the performance and design of a
packed column distillation unit with an azeotrope to the tray columns the author had prior experienced in operation
in the lab. This further evolved into developing a full design to be proposed for construction in the lab for eventual
student use.
Chemical System Definition
The chemical system central to the design is a binary mixture of water and isopropanol (i-Pr). This system has a
characteristic azeotrope and wildly varying relative volatility. The high degree of variance in the relative volatility at
lower concentrations of isopropanol is to be expected as the isopropyl group causes significant steric hindrance to
potential hydrogen bonds with the hydroxyl group [1]. This behavior is depicted in Figure 1 in the section on
thermodynamic models.
Overview of Design Process
The design process was largely heuristics based with guidance from the research mentor. Along the way, several
constraints on the design were encountered which may be summarized prior to the design method for sake of
simplicity.
Pedagogical Considerations
Given that the eventual purpose of the design was to function as a working unit operation for student use in the
senior laboratory course as well as to test the utility of the chosen modeling scheme, practical pedagogical
constraints and the concerns of students taking their laboratory courses using current equipment were taken into
consideration. Chief amongst those concerned was the physical capacity to operate the system in a wide enough
range of desired conditions to gather characterizable data. To address this issue, the system’s size was bounded by
the desire to allow for more experimental operations in the same amount of time, which meant the system would be
more sensitive to control manipulations, but would converge in a timely manner. Second was the desire to reduce
downtime between experimental operations. This was a broad concern but not as prevalent as many students were
not able to achieve multiple runs during the normally allotted time. This was addressed by surrounding the core
system with a recycle and waste management system. The pedagogical advantage of this was allowance for a larger
degree of measurability since the recycle system would avail the relevant data to students during the recycle
procedure.
Nominal Design Constraints and Initial Parameters
Several constraints were placed on the nominal design to satisfy physical and practical constraints inherent to its
proposed eventual construction in the Unit Operations Laboratory of the University Of Florida Department Of
Chemical Engineering. The design was limited to using a reasonable amount of electrical power and/or steam, fitting
within the Unit Operations Laboratory, and reducing costs where possible such that eventual construction was a
viable project.
Reduction of costs was applied systematically by determining the utility of spare materials and parts in the lab to the
design and by scaling down the system to the optimal configurations with lower associated costs.
Reasonable electrical power was determined based upon peak use of 90% of the maximum current available from a
standard wall socket at with approximately 10% loss of potential due to circuit efficiency. A standard wall socket is
regulated by circuit breaker and building voltage to provide up to 15 amperes rms at 115 volts rms [2]. As is shown
below, this translates to roughly 1.4KW of available power for the entire system.
PDC Design
Pavailable, system = (0.90 × 15 A𝑟𝑚𝑠 ) × ((1 − 0.10) × 115 V𝑟𝑚𝑠 ) = 1397.25 Watts
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Equation 1
Assuming that any process controls used are manual or pneumatic and removing from the system’s electrical power
limit the sufficient power to operate a computer of minimalist design (to be used for process control and data
recording), which was poorly estimated at an arbitrary 400W, leaves a reasonable limit of 1KW for the maximum
operating power of an electrically powered design.
Pavailable, heating = 1397.25 W − 400W = 997.25 Watts
Equation 2
In the course of designing the system, this created an operational pinch point that was later used as the selection
criteria for the means of heating the reboiler after the requisite power was determined.
The physical constraints of the Unit Operations Laboratory itself limited the system height, and therefore the column
height, to the height of the first floor of the lab, which was conveniently the largest available space and
approximately 20 feet high. Upon inspection of the first floor of the lab, it was discovered that the frame from a
previously dismantled double effect evaporator was available to house the design. The frame was 54 inches wide,
48 inches deep and 108 inches high. This effectively limited the core system diameter to roughly 4 ft.
Given the electrical power limit of 1KW, an initial arbitrary column diameter of 3 inches was chosen as a basis. The
packing material chosen was ¼ inch ceramic Raschig Rings as there was a surplus supply in the lab at the time and
using it would reduce costs. The nominal compositions for the material streams at the core system boundaries were
20mol% i-Pr for the feed, 10mol% i-Pr for the bottoms, and 60mol% i-Pr for the distillate. The internal conditions of
the system were specified as being at VLE with a system pressure of 1 atm.
Model Selection Criteria
Models were selected based primarily on a balance of the global expected inherent uncertainty and the closeness of
fit to the specific physical system being modeled. This general strategy was used to select the majority of the pure
component models used in the final design. However, some cases required a more in depth exploration into the
research that went into the formulation of the respective model. Accuracy became a concern when selecting metacorrelations or correlations built upon the results of subordinate correlations. As may be expected, this was most
encountered when selecting multicomponent models to describe the various physical subsystems involved in the
overall design.
Many of the models chosen to describe multicomponent behavior were abstract mixing rules, meta-correlations
constructed to be agnostic of the pure component subordinate correlations chosen as a basis. For example, the Van
der Waals and Wong-Sandler mixing rules are constructed such that their pure component basis is simply restricted
to the general type of correlation construction. For the Van der Waals mixing rule, any equation of state may be
used [3] whereas the Wong-Sandler mixing rule can use any model for the excess Gibbs energy of mixing model [4]or
excess Helmholtz energy of mixing at infinite pressure, as was its original formulation [5]. This appears to be a
generally constructive strategy [6], but it is the author’s opinion that blindly accepting a meta-correlation without
consideration of the subordinate correlations used tends to misrepresent the multicomponent model’s accuracy.
Given this reasonable constraint that the generalized meta-correlations selected for this design be previously tested,
the author consulted several works when selecting the multicomponent models and chose those that had been
tested using multiple subordinate correlations when possible. When the author could not locate a suitably tested
multicomponent correlation, the previous general heuristic was applied and the subordinate correlations specified
were employed when possible.
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Selection of Thermodynamic Properties Models
Several thermodynamic models were considered for this design. Since some degree of quantitative accuracy was a
desired goal, more complex models were chosen in lieu of those which may have been qualitatively sufficient. The
general calculation procedure used was to calculate the fugacity coefficient for each phase using a combination of
pure component models and mixing rules, then to use the 𝜙 − 𝜙 method to determine the properties of the
equilibrium states of the vapor and liquid phases [3] [7] [8].
Vapor Phase Model
The thermodynamic model used for the vapor phase was the Peng-Robinson-Stryjek-Vera-2 (PRSV-2) model with
literature binary coefficients used for the binary interaction parameters [9] [10]. This method affords a significant
increase in accuracy for VLE calculations over even the Peng-Robinson (PR) model. This was found to be due to the
extreme degree of non-linearity present in the equations governing VLE and the numerical method requisite in
determining stable VLE states [9] [10].
Liquid Phase Model
The thermodynamic model used for the liquid phase was based in the General NRTL activity model [11], with binary
coefficients estimated by UNIFAC [12]. While this may seem counterintuitive as activity models are typically used for
the 𝛾 − 𝜙 method [3], the careful choice of mixing rule allows for use of the much less complicated 𝜙 − 𝜙 method [5].
The UNIFAC estimated binary interaction parameters were sufficient for describing the chemical system’s behavior
upon comparison of the nominal system predictions with literature data [1] [13] [16].
Mixing Rules
Two mixing rules were used to obtain mixture thermodynamic properties, one for each respective phase. The Van
der Waals mixing rule was used to predict the vapor phase state and the Wong-Sandler model was used for the
liquid phase.
Van der Waals
This mixing rule was chosen for its relative simplicity over newer models which sacrifice significant computation time
for relatively small gains in accuracy [14]. It was sufficient that the choice of the PRSV-2 model over the PR model
brought the system behavior into a reasonably quantitative range of accuracy [15]. The Van der Waals mixing rule is
also thermodynamically consistent as it satisfies the quadratic second Virial coefficient condition (QSVC) [3].
Wong-Sandler
This mixing rule was chosen for its significant improvements in accuracy over previous models as well as its general
versatility [5]. It is independent of the chosen activity model used [8], which provided flexibility in how the
thermodynamic models were evaluated against the reference data. When used in combination with the General
NRTL model, it satisfies the QSVC condition [8]. This thermodynamic consistency was a characteristic the author
desired to maintain as a governing threshold during VLE calculations.
Evaluation of Thermodynamic Properties
As was previously mentioned, the 𝜙 − 𝜙 method, allowed by the Wong-Sandler mixing rule, was used to calculate
the VLE states of the nominal system [16]. The VLE conditions were calculated for 1000 evenly spaced compositions
including the pure components. This was accomplished using the UniSim Design software [16]. This data set formed
one of two components comprising the basis dataset used for all further calculations. The other half of the basis
dataset was the transport properties data calculated for each of the mentioned compositions. As may be seen in
Figure 1, the nominal design compositions are constrained by an azeotrope at roughly 67mol% i-Pr. As all nominal
compositions are below this limit, none were changed at this stage of the design. The T-XY diagram, Figure 2, was
revealing as at the entire system is specified as being at or below the normal boiling temperature of water with no
significant pressure drop across vessel walls.
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C3H7OH-H2O System X-Y Diagram
P = 1 atm
1
0.9
0.8
0.6
0.5
y
0.4
x
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x_C3H7OH
Figure 1: Water-Isopropanol Vapor-Liquid Equilibrium Plot
C3H7OH-H2O System T-X Diagram
P = 1 atm
100
98
T_Bubble, T_Dew (degrees C)
y_C3H7OH
0.7
96
94
92
90
T_Bubble
88
T_Dew
86
84
82
80
0
0.2
0.4
0.6
0.8
x_C3H7OH, y_C3H7OH
Figure 2: Water-Isopropanol System T-XY Diagram
1
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Selection of Transport Properties Models
Transport properties models were similarly chosen for their relative accuracy, but this constraint was allowed to
relax some as the transport properties were not involved in the VLE calculations [7]. The key distinction between the
regimes of accuracy tolerance is the degree of uncertainty introduced through feedback in iterative calculations. The
transport properties were involved primarily in feedforward calculations, which carry significantly less risk of solution
instability due to objective function uncertainty.
This change in how uncertainty is propagated may be seen by carrying out the systematic uncertainty analysis when
recursively evaluating a continued fractions expression to an arbitrary degree and then comparing the result with
the uncertainty propagated by evaluating the analytically derived solution that requires a single evaluation. This
example is sufficient to suggest the necessity of a higher standard of accuracy for thermodynamic equilibria
calculations as VLE solution techniques employ equations of a non-linearity well beyond that of a simple continued
fractions statement [17] [18].
As such, the default models present in UniSim [16] were consulted first and replaced or modified if needed.
Viscosity Model
The default modified Letsou-Stiel model present in UniSim was used for the viscosity model [16]. The data produced
by the modified Letsou-Stiel model qualitatively agreed very well with the reference data [1] [13] [20] [20] [21] [25]. The
resulting plot of liquid viscosity as a function of composition is given below in Figure 3.
C3H7OH-H2O System Liquid Viscosity vs X
Diagram
P = 1 atm
Liquid Viscosity x10^3 (Pa*s)
0.5
0.45
0.4
Liq. Viscosity
0.35
0.3
0.25
0
0.2
0.4
0.6
0.8
x_C3H7OH
Figure 3: Plot of Liquid Viscosity vs Composition
1
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Surface Tension Models
As was done with the viscosity, the surface tension model was left up to UniSim to compute and was then checked
against reference data for qualitative agreement [16]. The surface tension model had similarly good agreement with
the reference data [1] [13]. The plot of surface tension as a function of composition is given below in Figure 4.
C3H7OH-H2O System Surface Tension vs X
Diagram
P = 1 atm
60
Surface Tension x10^3 (N/m)
55
50
45
40
35
Surface Tension
30
25
20
15
0
0.2
0.4
0.6
0.8
1
x_C3H7OH
Figure 4: Plot of Surface Tension vs Composition
Thermal Conductivity and Dielectric Coefficient Models
The thermal conductivity and dielectric coefficient models were also allowed to be governed by UniSim [16]. They had
good qualitative agreement with the reference data [1] [13].
Diffusivity Models
The diffusivity models were selected based on ease of use and applicability to the system being studied.
Gilliland Correlation
The Gilliland correlation describes the effective diffusivities of gasses and was used to determine the diffusivities of
the vapor phase [19].
Wilke and Chang Correlation
Since the liquid phase cannot be treated in the same ideal manner as the vapor phase (for which most models begin
with the classical Stokes-Einstein relationship), the infinite dilution diffusivities are calculated and combined using a
mixing rule much the same way as the thermodynamics models are constructed. The Wilke and Change correlation
is used for non-polar to moderately polar substances. It is a good model for weakly polar substances dissolved in
polar substances, and was therefore used for the infinitely dilute isopropanol in bulk water [19].
Sitaraman et al. Correlation
This correlation is specifically recommended for infinitely dilute water in a bulk substance of weaker polarity,
therefore it was used for the infinitely dilute water in bulk isopropanol [19].
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Leffler and Cullinan Correlation
This correlation acts as the mixing rule that combines the pure substances’ behavior to describe the mixture. The
high degree of non-linearity relative to other available models was a concern, but was it was discovered upon
inspection that the uncertainty propagated would not likely be of concern to the final model [19]. This model did
correlate well with literature data within the range of conditions in the nominal design [27].
Selection of Flooding Model
While there were many good models to choose from, the model that made the most sense to use in the final design
was the definitive Sherwood et al. model. This model was constructed from experiments performed on a steam
rectification unit with the same nominal packing and internal conditions range as those chosen for the design being
discussed [20].
The alternate model used for qualitative analysis of system behavior was the far more general correlation by Piché et
al. [20]. This model was based on the use of an artificial neural network to correlate the behavior of a randomly
packed column over a wide range of conditions using a wide variety of packings. It is the author’s opinion that the
correlation produced may not have had enough subunits to satisfactorily capture the fully generalized nature of
packed systems in quantitative detail [21] and that there was sufficient accuracy within the validation data set to
warrant qualitative use prior to final selection of a nominal packing material [20].
Selection of Loading Model
The correlation by Piché et al. for loading point prediction was used in the same manner as the corresponding
flooding point model [22]. Since the loading behavior of a packed column does not quantitatively impact the
maximum power requirement of the reboiler, a qualitative description of the behavior is satisfactory for use in
locating reasonable limits of operation [23].
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Determination of Power Requirements
The power requirements for the core system were based on the calculated vapor rate at the flood point. This is
simply determined as the product of the flow rate and latent heat of vaporization.
Pfl = 𝜆𝑣𝑎𝑝 × V2,𝑓𝑙
Equation 3
The flooding power requirement as a function of column height was determined using the generalized correlation of
Piché et al. [20] and is shown in Figure 5 below.
Power at Flood (KW) vs Column Diameter (in.)
1/4" Ceramic Raschig Rings
80
70
y = 0.7972x2.0045
R² = 1
Power (KW)
60
50
40
Power at Flood (KW)
30
Power (Power at Flood (KW))
20
10
0
0
2
4
6
8
10
Column Width (in.)
Figure 5: Flooding Power vs Column Height for 1/4" OD Ceramic Raschig Rings
As may be seen in Figure 5, the power scales roughly as a function of column diameter squared and has a value of
approximately 7.2KW for a column with a 3 inch diameter. Projecting along the trend line, the column would have
to be 1 inch (at the nearest 1/16 inch) in diameter to reach the electrical power limit. This ruled out the use of
electrical power at the desired system size. There was also the accuracy of the models being used to predict the
flood point to consider when selecting a column diameter. Most flooding models are correlated such that the
predictions deviate significantly from observed system behavior when the ratio of the column diameter to packing
diameter falls below 30 [23]. Specifically, the model used for this preliminary power requirement estimate tends to
over predict the power required for random packings with a diameter less than ½ inch [20], but the qualitative
conclusions as to which power source should be used for heating were quite clear: steam heating.
Final determination of the required power for the reboiler was based on the correlation by Sherwood et al., which
was included in the final design model [20].
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Selection of Heat Transfer Models
Heat transfer models were chosen for their applicability to the various physical and chemical regimes in the core
system and then by the accuracy of the model with respect to said application.
Nusselt Model
The Nusselt model for condensation in a horizontal pipe was chosen to describe the condensation occurring in both
the reboiler (steam) and condenser (distillate) for its applicability to a wide range of conditions and its general
accuracy [3] [31].
Mostinski Model
The Mostinski model was chosen for its general applicability to the heat transfer occurring in the nucleate pool
boiling regime for pure fluids [24] [25] [33]. As will be explained further, the model chosen for describing the heat
transfer for the nucleate pool boiling regime in a multicomponent mixture requires pure component heat transfer
coefficients to work.
Modified Thöme and Shakir Model
The modified Thöme and Shakir model was originally considered for use due to its generally superior performance
relative to other correlations when considering the water isopropanol system [24]. However, a relatively small
modification allowed for a worthwhile increase in accuracy and was used in tandem [7].
Combined Model Evaluation and Heat Exchanger Sizing
The models for the reboiler and condenser were assembled using the series resistances paradigm shown below
𝑄𝑅𝐵 =
∑𝑗 ∆𝑇𝑗
𝑇i − 𝑇o
=
1
∆𝑟𝑤
1
∑𝑗 𝑅𝑗
+
+
ℎi 𝐴i 𝑘𝑤 𝐴𝑤 ℎo 𝐴o
Equation 4
where 𝑇 is temperature, 𝑟 is pipe radius, 𝐴 is area, ℎ is heat transfer coefficient, and 𝑘 is thermal conductivity [3] [7]
[26]
. The respective correlations were substituted into Equation 4 for both the reboiler and condenser, which were
then rearranged to produce the following respective non-linear objective functions of the length of pipe [3] [7]
1
𝜁
𝑓𝑜𝑏𝑗 (𝐿) = 𝛼 + 𝛽𝐿−3 − 𝛾𝐿 + 𝛿𝐿0.7 (1 + 𝜀 (1 − 𝑒𝑥𝑝 ( )))
𝐿
Equation 5
4
31
1
𝑓𝑜𝑏𝑗 (𝐿) = 𝐿3 + 𝛼𝐿30 + 𝛽𝐿3 + 𝛾
Equation 6
where all variables other than 𝐿 are compound expressions of other physical variables. Given the reasonably smooth
nature of these objective functions within the range of physically possible values for length (positive real numbers),
Newton’s method and successive substitution with physically plausible initial values were used to find the respective
solutions [3]. This approach produced consistent and reasonable results, as there were neither situations calling for
impractically sized heat exchangers encountered nor non-physical results produced. Evaluation of the size of the
required heat exchanging surface using the solutions from Equation 5 and Equation 6 is the first step in determining
the size of both the reboiler and the condenser.
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Initial Sizing of the Reboiler
With the length of the pipe to be used for heat exchange numerically solvable as a function of pipe radius, the next
step was to size the shell and to determine the pipe’s geometry relative to the shell. A minimum reboiler diameter
was determined by using a dual coil design for the pipe geometry with a single pipe diameter spacing maintained
within the coil. This design was chosen because it allowed for completely planar coil geometry and featured counter
current flow of the heat source in a cylindrical geometry. The planar geometry allows for greater flexibility in vertical
placement of the coil as it is only one pipe diameter thick, and the dual coil design also allows for placement of the
steam inlet and outlet in any position along the outside of the reboiler in the plane of the coil. The vertical
placement is important as nucleate pool boiling is theoretically based upon low or zero bulk flow conditions in most
treatments [7] [26]. The cylindrically oriented counter current flow of condensing steam provides for even heating of
the reboiler contents. The reboiler was initially sized for continuous operation of the core system. This meant that
the volume of the reboiler was irrelevant to the method used to predict the mass transfer behavior of the system.
Selection of Mass Transfer Models
Models for mass transfer were chosen to determine the effective specific area of the packing and the mass transfer
coefficients of the column. Determination of these values was discovered to be the most heavily involved step in
determining how the column would behave and how to size the final system [37] [38].
Onda et al. Correlations
The correlation for effective specific area by Onda et al. was chosen because the original research behind it was
performed on the same packing material being used for the nominal system design and because the correlation is
satisfactorily accurate for quantitative prediction [27]. The correlation for the interface mass transfer coefficients,
both 𝑘G and 𝑘L , by Onda et al. were similarly chosen for the same similarity in physical systems involved [27]. Follow
up work by Piché et al. attempting to generalize the prediction of packed column mass transfer was used to confirm
the quantitative utility of these models [28] and a review of mass transfer correlations by Wang et al. confirmed the
general qualitative accuracy of the chosen correlations relative to other possible choices in the context of the
intended nominal design [29].
Mass Transfer Behavior and Column Sizing
The overall mass transfer behavior was determined by translating from the interfacial mass transfer regime to the
overall mass transfer regime and then using the design integral for packed columns to size the column itself.
Translation from Interfacial to Overall Mass Transfer
Conversion of interfacial coefficients to overall coefficients was accomplished by taking advantage of the relationship
between the interfacial and overall transfer coefficients as may be seen in the following equation
1
1 𝑚′
=
+
𝐾𝑦 𝑘G 𝑘L
Equation 7
where 𝐾𝑦 is the vapor phase overall mass transfer coefficient, 𝑚′ is the slope of the equilibrium line on the XY
diagram shown in Figure 1, and 𝑘G and 𝑘L are the interfacial mass transfer coefficients as were previously defined [3]
[19] [23] [27] [29] [30]
. The overall mass transfer coefficient was only necessary for one phase to continue, though the
correlated value for both phases would be necessary to perform an internal check on the model’s accuracy. Only the
overall mass transfer coefficient for the vapor phase was calculated in the interest of time constraints.
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Design Integral
The design integral was subsequently used to determine the required height of packing material to yield the desired
nominal mass transfer. The equation for this is
𝑥𝐷
𝑥𝐷
𝑥𝐷
𝑑𝑦
𝑧 = ∫ 𝐻𝑜𝑦 ∗
= ∫ 𝐻𝑜𝑦 𝑑𝑁𝑜𝑦 ≈ 𝐻𝑜𝑦 ∫ 𝑑𝑁𝑜𝑦 ≈ 𝐻𝑜𝑦 𝑁𝑜𝑦
𝑦 −𝑦
𝑥𝐵
𝑥𝐵
𝑥𝐵
Equation 8
where 𝑧 is packing height, 𝑥𝐵 is reboiler composition, 𝑥𝐷 is distillate composition, 𝐻𝑜𝑦 is the vapor phase height of a
transfer unit (HTU), 𝑁𝑜𝑦 is the vapor phase number of transfer units (NTU), 𝑦 is the equilibrium vapor phase
composition, and 𝑦 ∗ is the vapor phase composition outside of the column in pseudo-equilibrium with the
equilibrium vapor phase composition. The HTU for the vapor phase is based on the correlation by Onda et al. [27].
Column Sizing and Calculated Mass Transfer Behavior
The design integral was evaluated in several different ways, in part, to investigate the variance in accuracy based
upon the methods expected to be known and used by students. The full integral was evaluated numerically to get
the most accurate results for the required height. This set the benchmark for all further analysis of the expected
effective mass transfer. Subsequently, the value for 𝑁𝑜𝑦 was calculated by integrating over the same interval and
used with Equation 8 to solve for the true average value for 𝐻𝑜𝑦 . After this, the integrated value for 𝐻𝑜𝑦 was
evaluated for comparison to the previous value by both integration and summation based averages. Finally, the
height of an equivalent theoretical plate (HETP) was calculated using
𝑚′𝑉
ln ( 𝐿 )
HETP = 𝐻𝑜𝑦
𝑚′𝑉
𝐿 −1
Equation 9
where 𝑉 is the vapor phase molar flow rate and 𝐿 is the liquid phase molar flow rate. The HETP may be further used
for comparison with tray columns operating under comparable constraints to evaluate their relative effective mass
transfer efficiencies.
Final Selection of Column
The column chosen to be used was already present in the lab and was selected because it has the same packing
material and the same diameter as the nominal design. The height was slightly different, but the model was
constructed such that this form of variation was easily compensated for.
Sizing the Condenser
With the mass transfer behavior determined, the condenser was sized to match or exceed the power entering at the
reboiler using the previously defined heat exchanger sizing equation (Equation 6) and the designated nominal
composition of the distillate, which was confirmed as feasible by the corresponding predictions for mass transfer
behavior. This safety consideration was well exceeded as the size called for by the nominal design was exceeded by
a factor of three in the smallest available unit present in the lab. It was decided that sub-cooling would be an
interesting pedagogical twist so the spare shell and tube heat exchanger was selected as the candidate condenser
for the final design.
PDC Design
P a g e | 15
Final Sizing of the Reboiler
As the system was designed from the beginning with an external means of recycling and waste management, the
column was operable in continuous, semi-batch, and batch modes. With the condenser sized, reboiler heat
exchanger sized, and mass transfer behavior determined, the final sizing of the reboiler was considered based on
batch operation. The volume of the reboiler was sized to contain enough fluid to operate for the entirety of a single
lab session, approximately four hours. To maximize boil off and thereby maximize possible separation, the reboiler
was designed in several flanged segments. The bottom section was set at a slightly larger diameter than was
determined by the initial sizing. This slightly oversized the heat exchanger, which consequently would challenge
students to properly control the system without flooding it. The middle section was set at a diameter that would
contain the required volume for a full lab session while fitting within the frame to be used for the system. Since the
liquid level in the reboiler was to be set to never fall below the interface of these two sections for normal operation,
the minimized boil off ratio for the given volume was achieved, which allowed for a maximum of possible separation.
The middle section was also tall enough to provide good resolution, and therefore a high resolving power, on a
calibrated sight glass spanning the height of the total reboiler. The top section acted simply as a cap to the reboiler
and interfaced with the column itself. This design was chosen such that the middle section could be removed to
inspect and service the heat exchanger. A schematic diagram of the final reboiler design is given in Appendix C.
Assembling the Completed Model
The final model was constructed within a Microsoft Office Excel 2010 workbook and setup such that many of the
design constraints and nominal values were variable user inputs. This provided significant flexibility in selecting
components and in determining the final nominal design. A static copy of the final design is given in Appendix A and
the file is available upon request from the author.
Description of Nominal System Design and Behavior
Column and Packing Material
The final nominal design is center around a core unit with a 6 ft tall, 3 inch inner diameter borosilicate glass column
randomly packed with ¼ inch Raschig Rings.
Reboiler
The reboiler has a nominal volume of 110 USGal. Its heating section is 12 inches in diameter and is 8 inches tall. The
middle section is 3 ft in diameter and is 2 ft tall. The top section has a 3 inch diameter flanged attachment and the
bottom section has a 1 inch diameter outlet. The heat exchanger is made of type K, ½ inch NPS copper pipe. The
minimum exchanger length is 1.05 ft which provides 0.172 sqr ft of exchanger area. The minimum diameter of the
reboiler is 8.2 inches.
Condenser
The condenser is a shell and tube design with an 8.33 inch ID aluminum shell and 15 I inch ID steel tubes. The
minimum length required is 10.2 inches which produces a minimum exchange area of 32 square inches.
Nominal Operation
The nominal core system operates continuously at 50% of the flooding power. The feed is 20 mol% i-Pr flowing at
10.4 USGPH into the reboiler. The bottoms is 10 mol% i-Pr flowing at 6.6 USGPH from the reboiler recycle return
line. The Distillate is 60 mol% i-Pr flowing at 3.9 USGPH from the reflux return line. The column has a 23.1% overall
“average tray efficiency,” 6.65 inch HTU, and 3.42 NTU corresponding to a 1.89 ft minimum required height.
PDC Design
P a g e | 16
Nominal Lab Session
The nominal lab session is predicted to include up to five continuous runs or 3 batch runs, and can accommodate
runs lasting the entirety of the lab session. The recycle and waste management system was designed such that a
downtime of as little as 8 minutes is expected between runs to pump from a pre-mixer to the supplying feed tank.
Concluding Remarks
The final design includes significant predicted improvements over the tray columns present in the lab. The design is
based upon sound correlations as verified by the literature data consulted but still suffers from the cumulative
propagation of small but significant error. While this was minimized by the careful selection of the correlations
chosen, the authors confidence in the numbers produced is cautiously estimated as ±20% and guessed to be as low
as ±10%. The author feels the experience was very rewarding as the process of synthesizing a full design and
performing each of the concomitant steps was particularly illuminating of the challenges involved in accurate
process design.
Acknowledgements
The author would like to acknowledge Dr. Lewis Johns for his guidance, Dr. Ranga Narayanan for his patience, and
Dr. Spyros Svoronos for his encouragement and advice. The author would also like to acknowledge the University of
Florida and its Department of Chemical Engineering.
PDC Design
P a g e | 17
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of Multicomponent Mixtures," Trans IChemE, Part A, Chemical
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PDC Design
P a g e | 18
Appendix A: Static Description of the Nominal Core System Description
The following is a static copy of the model as was constructed in the Excel workbook.
Manual Inputs
Physical Consts
g
9.81 m/s^2
sigma_crit
0.061 N/m
FW_PrOH
60.1 Kg/Kgmol
FW_H2O
18.02 Kg/Kgmol
P_c_PrOH
47.6 bar-abs
P_c_H2O
221.2 bar-abs
Packing Data
Type
Raschig Ring
Material
Ceramic
d_p
0.25 in.
= d_p
0.00635 m
a_p
330 m^2/m^3
epsilon
0.7 m^3/m^3
N_p
50000 m^-3
NRTL-PR VLE Data
alpha_12
0.326 alpha_21
0.326
beta_12
833.168 beta_21
20.06
Pure Fluid Data @ Normal BP
PrOH dHvap
659200 J/Kg
H2O dHvap
2213000 J/Kg
PrOH Vbar
8.55E-02 m^3/Kgmol H2O Vbar
1.90E-02 m^3/Kgmol
Mass Transfer Data
D_AB_inf
1.13228E-10 m^2/s
D_BA_inf
1.81888E-07 m^2/s
D_V (83.22C)
2.00922E-05 m^2/s
Desired Column Specs and Desired Overall Performance (Continuous and Batch)
P_RB
1 atm
R_D
1 R_D (Batch)
z_desired
2m
x_D
0.6 x_B_0 (Batch)
D_c
3 in.
x_F
0.2 x_B_1 (Batch)
% Of Flood
50 %
x_B
0.1
Reboiler Physical and Sizing Correlation Parameters
beta_L
0.0003 m/s
B_o
1
b
0.1011
K_p
400 W/m*K
Pipe OD
0.625 in.
Pipe NPS
0.5 in.
Pipe t
0.049 in.
Reboiler Steam Properties
T_s
150 C
P_s
4.7572 bar-abs
rho_c
917.06 Kg/m^3
rho_s
2.5454 Kg/m^3
dHvap
2098.3 KJ/Kg
mu_c
0.000182 Pa*s
K_c
0.6821 W/m*K
Condenser Physical and Sizing Correlation Parameters
Pipe OD
1 in.
Pipe NPS
1 in.
Pipe t
0.0625 in.
K_p
12 W/m*K
Shell ID
8.329 in.
# of Tubes
15
Condenser Coolant Properties
T_c
25 C
Q_c
5 GPM
rho_c
997 Kg/m^3
mu_c
0.001 Pa*s
K_c
0.58 W/m*K
Cp_c
4186 J/(Kg*K)
Lab Session Constraints
t_lab
4 hrs
t_mix
20 min
t_shutdown
10 min
t_startup
10 min
t_transition
20 min
# trials desired
4 trials/lab
Physical Data
dP @ Flood
Average Diffu
avg D_L
Numerical Pac
Z_t
Transfer Unit
Noy* (int)
avg Hoy*(sum
avg HETP_y*
Reboiler Heat
A
D
L_i
L_max
dr
L_RB
A_RB
U_RB
1 UA_RB
0.6 m_s
0.1 Reboiler Mini
B
a_max
a_0
a_0+Pi
err
D_RB
Condenser Co
A
L_i
L_max
dr
L_c
A_c
U_c
Average Cont
avg V
avg L
avg D
avg F
avg B
avg L/V
avg F/D
avg F/B
avg D/B
PDC Design
Calculated Inputs
Overall Performance
Column Specs
Mass Transfer Data
L/V
0.5 A_c
0.004560367 m^2
c
Reboiler Heat Exchanger Parameters
r_o
0.0079375 m
r_i
0.0066929 m
Condenser Physical Parameters
r_s
0.1057783 m
r_o
0.0127 m
r_i
0.0111125 m
m_c
0.314504629 Kg/s
D_H
0.059199062 m
Re_o
6764.291798
Pr_o
7.217241379 f_o
0.035235448 Nu_o
55.44369607
Lab Session Constraints (Assuming Equal Length Trials Operating in Steady State or Batch)
t_trial_min
20 min
t_trial_max
35 min
P a g e | 19
Vol_max_F
Vol_max_B
2 Lab Session Co
Vol_trial_F
Vol_trial_B
Lab Session Co
Vol_trial_F
Vol_trial_B
Column Volum
V_col
V_col_void
Relative Volat
PDC Design
P a g e | 20
Calculated Outputs
Reboiler Volu
Manual Inputs
Q_RB,op
6.336012623 KW
K_wall_RB
h_i_RB
avg D_V
1.98755E-05 m^2/s
T_i_RB
t_wall_RB
% Z_desired
28.85036374 % dZ_desired -71.14963626 z_RB_max
Physical Data
dP @ Flood
6.135359619 inH2O
Average Diffusivity Data
avg D_L
1.92398E-09 m^2/s
Numerical Packing Height
Z_t
0.577007275 m
Transfer Unit Data
Noy* (int)
3.418178223
avg Hoy* (int) 0.154451178 m
avg Hoy*(sum) 0.15480292 m
Hoy* (z/Noy*) 0.168805497 m
avg HETP_y*
0.20732365 m
avgc HETP_y*
m
Calculated Inp
Reboiler Heating Requirements Data and Numerical Evaluation Values
r_i_RB_min
A
0.00052519 B
9.27024E-05 C
3.38437E-06
D
9.89475E-05 E
0.273450087 F
0.259054481
r_o_RB
L_i
0.5 erth
1E-12 L_min
0
L_max
100 L_0
0.320425218 err
9.86838E-13 9.86904E-13 Calculated Ou
dr
0.1 dL
9.86838E-14 L_x
0.320425218
V_RB_tot
L_RB
0.320425218 m
= 1.051488597 ft
V_RB_tot
A_RB
0.015980498 m^2
= 0.172086203 ft^2
SA_i_RB
U_RB
5942.336886 W/m^2*K = 1046.058706 Btu/hr*ft^2*F Re_c
1578.130277 Q_i_RB
UA_RB
94.96149979 W/K
Reality Check: Re_c <= 2100?
m_s
0.003019593 Kg/s
= 23.97387983 lb/hr
TRUE
Column Insula
Reboiler Minimum Diameter/Crossection Area (Dual Spiral Design) and Numerical Evaluation Values Manual Inputs
B
92.52463625 erth
1E-12 a_i
4.319689899
K_wall_col
a_max
100 a_min
1.570796327 dr
1
h_i_col
a_0
4.814756975 f(a)
25.95205249 f'(a)
51.94262328
T_i_col
a_0+Pi
7.956349628 f(a+Pi)
66.57258376 f'(a+Pi)
133.1601879
t_wall_col
err
8.60853E-13 da
8.60853E-13 a_x
4.814756975
Calculated Inp
D_RB
0.208444131 m
CrossA_RB
0.03412473 m^2
r_i_col
Condenser Cooling Requirements Data and Numerical Evaluation Values
r_o_col
A
0.010458752 B
0.000459671 C
0.00198224
Calculated Ou
L_i
0.5 erth
1E-12 L_min
0
Q_i_col
L_max
10 L_0
0.258521782 err
9.43051E-13
dr
0.1 dL
9.43051E-14 L_x
0.258521782
Pipeline Insul
L_c
0.258521782 m
UA_c
7.629634611 W/K
Manual Inputs
A_c
0.020629121 m^2
Re_V
687.1375231
K_wall_pipe
U_c
369.8477748 W/m^2*K
Reality Check: Re_V <= 2100?
TRUE
h_i_pipe
Average Continuous Input/Output Flow Rate Data
T_i_pipe
avg V
0.138113355 mol/s
F-D-B ( ? = 0 )
0
TRUE
t_wall_pipe
avg L
0.069056677 mol/s
=
0.064640941 USGPM
= 3.878456459 USGPH
D_pipe
avg D
0.069056677 mol/s
=
0.064640941 USGPM
= 3.878456459 USGPH
L_pipe
avg F
0.345283387 mol/s
=
0.173660125 USGPM
= 10.41960749 USGPH
Calculated Inp
avg B
0.27622671 mol/s
=
0.109907409 USGPM
= 6.594444556 USGPH
r_i_pipe
avg L/V
0.5
avg Q_L/Q_D
1
r_o_pipe
avg F/D
5
avg Q_F/Q_D 2.686534604
Calculated Ou
avg F/B
1.25
avg Q_F/Q_B 1.580058396
Q_i_pipe
avg D/B
0.25
avg Q_D/Q_B 0.588139975
Q_i_p/L_p
PDC Design
Calculated Outputs (Continued)
Calculated Batch Operation Performance (Rayleigh Still Model)
x_B Integral -3.502237229 B/B_0
0.0301299
Lab Session Constraints: Continuous Operation Max Total Volumes
Vol_max_F
41.67842995 USGal
Vol_max_D
15.51382583 USGal
Vol_max_B
26.37777822 USGal
dVol_(F-D-B) -0.213174109 USGal
Lab Session Constraints: Continuous Operation Max Trial Volumes per Trial at Steady State
Vol_trial_F
6.078104368 USGal
Vol_trial_D
2.262432934 USGal
Vol_trial_B
3.846759324 USGal
dVol_(F-D-B) -0.031087891 USGal
Lab Session Constraints: Continuous Operation Min Trial Volumes per Trial at Steady State
Vol_trial_F
3.473202496 USGal
Vol_trial_D
1.29281882 USGal
Vol_trial_B
2.198148185 USGal
dVol_(F-D-B) -0.017764509 USGal
Column Volumetric Physical Values (Desired Dimensions)
V_col
0.009120735 m^3
SA_col_dry
3.009842426 m^2
V_col_void
0.00273622 m^3
= 0.710706594 USGAL
Relative Volatilities and Corresponding Geometric Means
Point Values
Geo. Avg. Values
alpha_D
1.160258913
alpha_avg
3.219020465
alpha_F
4.756859682
alpha_avg_D 2.349295393
alpha_B
8.93084521
alpha_avg_B 6.517881366
Number of Equivolent Theoretical Plates and Corresponding Min. Values
Minimum Values
Calculated Values
N_min
2.226277175
N_Z_c
2.783123268
N_min_D
2.097795407
N_Z_d
9.646752785
N_min_B
0.432600083
Avg. Efficiencies at the Calculated and Desired Column Heights (Fenske Eqn.)
Calculated Height
Desired Height
e_a
0.799920435
E_a
0.230779955
e_D
0.753755837
E_D
0.217461301
e_B
0.432600083
E_B
0.432600083
Ratio of Respective Efficiencies (a possibel measure of column effectiveness)
E_a/e_a
0.288503637 E_D/e_D
0.288503637 E_B/e_B
1
P a g e | 21
Total Required
Q_tot
m_s
Re_c
PDC Design
P a g e | 22
Reboiler Volume/Insulation Sizing and Associated Power Loss, Assuming Min. Reboiler Coss-Area
Manual Inputs
K_wall_RB
16.5 W/m*K
K_ins_RB
0.021 W/m*K
h_i_RB
1000 W/m^2*K
h_o_RB
10 W/m^2*K
T_i_RB
100 C
T_o_RB
25 C
t_wall_RB
0.005 m
t_ins_RB
0.0762 m
z_RB_max
0.5 m
V_RB/V_tot_F
0.5 v/v
Calculated Inputs
r_i_RB_min
0.104222066 m
r_o_RB
0.185422066 m
V_RB_liq
r_ins_RB
r_i_c
0.080230978 m^3
0.109222066 m
0.0381 m
Calculated Outputs (Assuming Minimized SA_RB)
V_RB_tot
0.017062365 m^3
= 4.431783135 USGAL
V_RB_tot
0.0802944 m^3
= 20.85568838 USGAL
SA_i_RB
0.391112369 m^2
Q_i_RB
10.42943256 W
Q_i_RB/Q_RB 0.164605615 %W/W
Column Insulation Sizing and Associated Power Loss
Manual Inputs
K_wall_col
1.05 W/m*K
K_ins_col
h_i_col
1000 W/m^2*K
h_o_col
T_i_col
100 C
T_o_col
t_wall_col
0.00635 m
t_ins_col
Calculated Inputs
r_i_col
0.0381 m
r_ins_col
r_o_col
0.09525 m
Calculated Outputs
Q_i_col
25.12248517 W
Q_i_col/Q_RB
0.021 W/m*K
10 W/m^2*K
25 C
0.0508 m
0.04445 m
0.39650308 %W/W
Pipeline Insulation Sizing and Associated Power Losses
Manual Inputs
K_wall_pipe
16.5 W/m*K
K_ins_pipe
0.04 W/m*K
h_i_pipe
1000 W/m^2*K
h_o_pipe
10 W/m^2*K
T_i_pipe
100 C
T_o_pipe
25 C
t_wall_pipe
0.00635 m
t_ins_pipe
0.0254 m
D_pipe
0.75 in
L_pipe
3.6576 m
=
12 ft
Calculated Inputs
r_i_pipe
0.009525 m
r_ins_pipe
0.015875 m
r_o_pipe
0.041275 m
Calculated Outputs
Q_i_pipe
65.1731983 W
Q_i_pipe/Q_RB 1.028615348 %W/W
Q_i_p/L_p
17.81856909 W/m
PDC Design
Total Required Reboiler Power Required (Including all Accounted Losses)
Q_tot
6.436737739 KW
Q_RB/Q_tot
98.43515271 %W/W
m_s
0.003067597 Kg/s
= 24.35499837 lb/hr
Re_c
1603.218193 Reality Check: Re_c <= 2100?
TRUE
P a g e | 23
PDC Design
Appendix B: Diagram of Core System
P a g e | 24
PDC Design
Appendix C: Reboiler Design Schematic
P a g e | 25