CHEMICAL ENGINEERING TRANSACTIONS 

VOL. 81, 2020 

A publication of 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Petar S. Varbanov, Qiuwang Wang, Min Zeng, Panos Seferlis, Ting Ma, Jiří J. Klemeš 

Copyright © 2020, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-79-2; ISSN 2283-9216 

Non-Linear Programming Distillation Model for Simultaneous 

Process Optimisation 

Keat Ping Yeoh, Chi Wai Hui* 

Department of Chemical and Biological Engineering, The Hong Kong University of Science and Technology, Clear Water 

Bay, Kowloon, Hong Kong SAR, China 

kehui@ust.hk 

Distillation columns are prevalent process units used to purify chemicals. However, they consume significant 

amounts of energy for heating and cooling. A rigorous non-linear programming (NLP) distillation model where 

mass, equilibrium, summation and heat (MESH) equations are applied to each stage is proposed to be used in 

conjunction with existing Heat Integration models for simultaneous process optimisation to reduce energy 

consumption. In the NLP model, a continuous variable is used for each stage to determine whether a stage is 

active or inactive. This variable controls whether there are any changes in stream properties as a stream passes 

through a stage. It also enforces the equilibrium constraint for streams exiting active stages. The continuous 

variable mimics a binary variable as it only takes on values of 0 or 1 in an optimal solution. 

The distillation model and a Heat Integration model for a multi-stream heat exchanger (MHEX) were 

implemented in GAMS with a case study on the separation of air consisting of N2, O2 and Ar. Analysis of the 

model performance showed that it achieved convergence in a short time (6 min for a model with 2,161 variables 

and 25,260 equations) even with crude initialisation methods. Results of the case study showed that the energy 

requirement per unit mass of oxygen product is not minimized at 100 % oxygen recovery. The average oxygen 

recovery was around 96 %. Optimisation of the case study on an air separation unit (ASU) reduced energy 

requirement by 5.4 % for some cases. 

1. Introduction

Distillation columns are energy-consuming process units used to purify products. Heat integration may be the 

key to reducing the energy consumption of distillation systems. More energy savings may be realized if an entire 

distillation system, including the heat recovery unit, is optimised simultaneously in an equation-oriented (EO) 

environment, as opposed to using sequential modular methods. Pinch Analysis is one method of Heat 

Integration which may be used to maximise the potential of heat recovery in distillation systems. In Pinch 

Analysis, the minimum cooling and heating utility requirements are identified given a minimum temperature 

approach in a heat recovery system comprised of selected process streams. However, Pinch Analysis is usually 

applied after a process has been designed. This sequential method of Heat Integration may result in wasted 

potential to reduce energy consumption. Duran and Grossmann (1986) pioneered an EO method for Pinch 

Analysis which can be applied to simultaneous optimisation. The method involved the use of a max operator, 

which proved to be challenging to commercial solvers due to its non-smooth nature. Subsequently, different 

methods of replacing the max operator were developed, including a smoothing approximation used in the same 

work by Duran and Grossmann, and the use of binary variables in a mixed integer non-linear programming 

(MINLP) formulation as well as an NLP model using the concept of pseudo temperatures by Hui (2014). 

With the development of equation-oriented Heat Integration models, it then became possible to simultaneously 

optimise an entire distillation system comprised of distillation columns and a heat recovery network or MHEXs. 

However, simultaneous optimisation of distillation columns with Heat Integration results in large model sizes 

with many infeasibilities, which may lead to premature termination of the solver. The modelling of distillation 

columns may require discrete variables to represent the number of stages when the number of stages is not 

fixed, leading to further difficulties in solving the model as an MINLP formulation such as the one by Farkas et 

al. (2008). Other works have utilized shortcut distillation models (Yeoh et al., 2019) or developed rigorous NLP 

 
 
 
 
 
 
 
 
 
 
                                                                                                                                                                 DOI: 10.3303/CET2081096 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 30/04/2020; Revised: 20/05/2020; Accepted: 29/05/2020 
Please cite this article as: Yeoh K.P., Hui C.W., 2020, Non-Linear Programming Distillation Model for Simultaneous Process Optimisation, 
Chemical Engineering Transactions, 81, 571-576  DOI:10.3303/CET2081096 
  

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distillation models (Kraemer et al., 2009) to circumvent the need to use an MINLP formulation. However, shortcut 

models may not be able to accurately capture the behaviour of distillation columns. Another rigorous NLP 

distillation model developed by Dowling and Biegler (2015) appears to be robust and effective in conducting 

flowsheet optimisation with Heat Integration and complex thermodynamic methods, showing the benefits of 

using a rigorous NLP model to represent the distillation process when used with Heat Integration.  

In this work, an alternative formulation for an NLP-based distillation model is proposed that may be used with 

Heat Integration methods in simultaneous process optimisation. The novel NLP model may be more robust than 

previous ones as it has less variables. A case study on the optimisation of an ASU consisting of two distillation 

columns and a MHEX was conducted to test the robustness and effectiveness of the novel NLP distillation 

model in flowsheet optimisation. 

2. Methodology

This section provides details on the formulation of the NLP distillation model and supporting models such as the 

Heat Integration model. Other information, such as the thermodynamic module and the flowsheet of the case 

study are also mentioned here. Assumptions and where to find parameters are also included in this section. 

2.1 NLP distillation model formulation 

Traditionally, distillation columns are modelled as a series of stages where flash operations occur. The inlet and 

outlet streams and relevant properties of a typical stage in a distillation column are shown in Figure 1. Liquid 

streams are saturated liquid at the bubble point, while vapour streams are saturated vapour at the dew point. 

Figure 1: Representation of streams and relevant stream properties of a typical stage in a distillation column 

In Figure 1, f represents the molar flowrates, x and y represent the liquid and vapour composition of component 

i, T and P represent the temperature and pressure of the stream, while H represents the enthalpy of the stream. 

L and V show whether the streams are liquid or vapour and n represents the stage where the stream exits from. 

An active stage is a stage where the outlet stream properties differ from those of the inlet. The liquid and vapour 

outlet streams of an active stage are in equilibrium with each other. Inactive stages are stages where the outlet 

stream properties are the same as those of the inlet. The constraint where the liquid and vapour outlet streams 

are in equilibrium with each other does not apply to inactive stages and needs to be relaxed. Since the number 

of active stages is an optimisation variable and is not known a priori, a surplus of stages will first be defined. A 

continuous variable is used to activate or deactivate the stages. 

MESH equations such as the ones shown below are applicable to both active and inactive stages.   

𝑓𝐿,𝑛−1 + 𝑓𝑉,𝑛+1 = 𝑓𝐿,𝑛 + 𝑓𝑉,𝑛 ∀ 𝐿 ∈ 𝐿𝑖𝑞;  𝑉 ∈ 𝑉𝑎𝑝; 𝑛 ∈ 𝑁 (1) 

𝑓𝐿,𝑛−1𝑥𝑖,𝑛−1 + 𝑓𝑉,𝑛+1𝑦𝑖,𝑛+1 = 𝑓𝐿,𝑛𝑥𝑖,𝑛 + 𝑓𝑉,𝑛𝑦𝑖,𝑛 ∀ 𝐿 ∈ 𝐿𝑖𝑞;  𝑉 ∈ 𝑉𝑎𝑝; 𝑛 ∈ 𝑁; 𝑖 ∈ 𝐼 (2) 

𝐻𝐿,𝑛−1 + 𝐻𝑉,𝑛+1 = 𝐻𝐿,𝑛 + 𝐻𝑉,𝑛 ∀ 𝐿 ∈ 𝐿𝑖𝑞;  𝑉 ∈ 𝑉𝑎𝑝; 𝑛 ∈ 𝑁 (3) 

The difference between an active and inactive stage lies in whether the flowrate, composition or temperature 

change. The following set of complementarity constraints are used to control whether a stage is active. 

(1 − 𝑍𝑛)(𝑓𝐿,𝑛 − 𝑓𝐿,𝑛−1) = 𝜀𝑛 ∀ 𝐿 ∈ 𝐿𝑖𝑞; 𝑛 ∈ 𝑁 (4) 

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(1 − 𝑍𝑛)(𝑥𝑖,𝑛 − 𝑥𝑖,𝑛−1) = 𝜀𝑛  ∀ 𝑛 ∈ 𝑁; 𝑖 ∈ 𝐼 (5) 

(1 − 𝑍𝑛)(𝑇𝐿,𝑛 − 𝑇𝐿,𝑛−1) = 𝜀𝑛 ∀ 𝐿 ∈ 𝐿𝑖𝑞; 𝑛 ∈ 𝑁 (6) 

Zn is a continuous variable with a value between 0 and 1. It is used to activate or deactivate a stage as necessary. 

𝜀 is a slack variable with a lower limit of 0. The summation of 𝜀𝑛 is added to the objective function to be minimized 

and it’ll take on a value of 0 in optimal solutions. From Eq(4) to Eq(6), whenever any one of the stream properties 

change, Zn must take on a value of 1 in order to force the left-hand side of the equations to be 0 to satisfy the 

equality constraint. In this way, stages where Zn = 1 are active stages where the stream properties change. 

Conversely, whenever the stream properties do not change, Zn could take on any value, as the left-hand side 

of the equation will always be equal to 0. However, as the following constraints also apply, it is not physically 

possible for Zn to take on a value of 1 for an inactive stage. 

This formulation where zero-flowrates do not occur circumvents a problem highlighted in Grossmann et al. 

(2005), where MESH equations are reduced when inlet and outlet flows are non-existent, leading to 

convergence failure. Addition of the slack variable was also done to avoid this problem, as 0 x 0 values are 

possible within the complementarity constraints in Eq(4) to Eq(6). Many of these characteristics to avoid singular 

equations are found in (Dowling and Biegler, 2015) but it can be observed that the novel model has less 

variables, as bypass streams do not need to be defined for each stage. 

Eq(4) to Eq(6) are not required for the vapour streams, as the vapour stream properties will be determined by 

the MESH equations. The change in H, enthalpy, is not included because it is calculated from other properties. 

Change in pressure is not considered either as the outlet stream pressures will be controlled by other equations. 

As mentioned before, the liquid and vapour outlets are in equilibrium for an active stage but not for an inactive 

one. The following set of equations are used to enforce the equilibrium constraint whenever a stage is active. 

𝑦𝑖,𝑛 ≥ 𝐾𝑒𝑞,𝑖,𝑛𝑥𝑖,𝑛 − (1 − 𝑍𝑛)𝑀 ∀ 𝑛 ∈ 𝑁; 𝑖 ∈ 𝐼 (7) 

𝑦𝑖,𝑛 ≤ 𝐾𝑒𝑞,𝑖,𝑛𝑥𝑖,𝑛 + (1 − 𝑍𝑛)𝑀 ∀ 𝑛 ∈ 𝑁; 𝑖 ∈ 𝐼 (8) 

𝐾𝑒𝑞,𝑖,𝑛 =
𝑃𝑠𝑎𝑡,𝐿,𝑖,𝑛

𝑃𝑉,𝑛
 ∀ 𝐿 ∈ 𝐿𝑖𝑞;  𝑉 ∈ 𝑉𝑎𝑝; 𝑛 ∈ 𝑁; 𝑖 ∈ 𝐼 (9) 

Where 𝐾𝑒𝑞,𝑖,𝑛 is the equilibrium constant. In this work, it is calculated from the saturated pressure of the liquid 

and the vapour pressure following Raoult’s Law in Eq(9). M is a sufficiently large scalar. 

Whenever Zn = 1, indicating an active stage, Eq(7) and Eq(8) are effectively equal to Eq(10). 

𝑦𝑖,𝑛 = 𝐾𝑒𝑞,𝑖,𝑛 𝑥𝑖,𝑛 ∀ 𝑛 ∈ 𝑁; 𝑖 ∈ 𝐼 (10) 

As mentioned before, it is not possible for Zn to take on a value of 1 for an inactive stage. This is because 

fulfilling Eq(10) without any changes in stream properties would require the inlet liquid and vapour streams to 

already be in equilibrium prior to entering the stage. Such a point is known as a Pinch point, and according to 

Westerberg and Wahnschafft (1996), an infinite number of stages is needed to go through the Pinch Point. 

Since the liquid and vapour outlets of an inactive stage cannot be in equilibrium, (1-Zn) cannot take on the value 

of 0, and (1-Zn) multiplied by M is used to relax the equilibrium constraint for inactive stages.  

Other than being in equilibrium with each other, another constraint where the temperature of the liquid and 

vapour outlet are equal applies to active stages. The constraint is implemented via Eq(11) and Eq(12). 

𝑇𝐿,𝑛 ≥ 𝑇𝑉,𝑛 − (1 − 𝑍𝑛 )𝑀 ∀ 𝐿 ∈ 𝐿𝑖𝑞;  𝑉 ∈ 𝑉𝑎𝑝; 𝑛 ∈ 𝑁 (11) 

𝑇𝐿,𝑛 ≤ 𝑇𝑉,𝑛 + (1 − 𝑍𝑛 )𝑀 ∀ 𝐿 ∈ 𝐿𝑖𝑞;  𝑉 ∈ 𝑉𝑎𝑝; 𝑛 ∈ 𝑁 (12) 

Similar to the implementation of the equilibrium constraint, Eq(11) and Eq(12) ensure that the outlet 

temperatures are equal when Zn is 1, and the constraint is relaxed otherwise. 

The novel NLP distillation model also includes pressure drop across active stages. Pressure drop is 

implemented via Eq(13) and Eq(14). The pressure of liquid and vapour streams leaving an active stage are also 

equal. This is implemented by Eq(15) and Eq(16) for Zn = 1, and relaxed when Zn is not 1. 

𝑃𝐿,𝑛 = 𝑃𝐿,𝑛−1 − 𝑍𝑛∆𝑃 ∀ 𝐿 ∈ 𝐿𝑖𝑞; 𝑛 ∈ 𝑁 (13) 

𝑃𝑉,𝑛 = 𝑃𝑉,𝑛+1 − 𝑍𝑛 ∆𝑃 ∀ 𝑉 ∈ 𝑉𝑎𝑝; 𝑛 ∈ 𝑁 (14) 

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𝑃𝐿,𝑛 ≥ 𝑃𝑉,𝑛 − (1 − 𝑍𝑛)𝑀 ∀ 𝐿 ∈ 𝐿𝑖𝑞;  𝑉 ∈ 𝑉𝑎𝑝; 𝑛 ∈ 𝑁 (15) 

 (16) 

∆𝑃 refers to a fixed value of pressure drop. While Zn can take on any value except 1 for an inactive stage, the 

pressure drop equations would force it to take on a value of 0 whenever the objective of the optimisation is to 

reduce energy consumption. In an energy consumption minimization problem, the optimal value would be one 

without unnecessary pressure drop for an inactive stage that does not carry out a flash operation. The NLP 

model is able to mimic an MINLP model since Zn only takes on binary values in an optimal solution.  

2.2 Heat Integration model 

The MHEX model used in the case study is modified from the NLP Heat Integration model proposed by Hui 

(2014). This model was selected instead of the Multi-M model found in the same work in order to solve the 

optimisation problem as an NLP problem instead of MINLP. The original NLP model formulation encompasses 

Eq(17) to Eq(29) in (Hui, 2014). As the original model was used for utility targeting in HEN, Eq(28) and Eq(29) 

from Hui (2014) are modified to the following equations. 

𝑄𝑆𝑂𝐴𝑘 (𝑥) ≥ 𝑄𝑆𝐼𝐴𝑘 (𝑥) (17) 

Ω(𝑥) = 0 (18) 

The equations are modified in this way because there are no hot or cold utilities. Eq(18) enforces energy balance 

for the streams entering and exiting the MHEX. 

2.3 Thermodynamic module 

An ideal thermodynamic module was employed to calculate stream properties such as enthalpy and vapour-

liquid equilibrium. The ideal thermodynamic module utilizes equations and parameters from the IDEAL method 

available in Aspen Plus V11. For example, Eq(19) is used to calculate the ideal gas specific heat capacity. 

𝐶𝑃,𝑖 = 𝐶𝑜1,𝑖 + 𝐶𝑜2,𝑖 (
𝐶𝑜3,𝑖 /𝑇

sinh (𝐶𝑜3,𝑖 /𝑇)
)

2

+ 𝐶𝑜4,𝑖 (
𝐶𝑜5,𝑖 /𝑇

cosh (𝐶𝑜5,𝑖 /𝑇)
)

2

 ∀ 𝑖 ∈ 𝐼 (19) 

Where Co1 to Co4 are component-specific parameters. In this work, 𝐶𝑃,𝑖  is assumed to be constant and equal to 

Co1,i due to the complexity of the sinh and cosh operators in Eq(19). This simplification does not greatly affect 

the calculation of CP,i, as the contributions of the second and third terms of Eq(19) are negligible compared to 

the first term within this study. 

2.4 Details of the case study and models of the auxiliary equipment 

Figure 2 shows the flowsheet used in the case study. The ASU shown here uses the double-column 

configuration, found to be the best in (Dowling and Biegler, 2015). Optimisation of the flowsheet is conducted at 

different oxygen product purities with the objective of minimizing energy consumption per kg of oxygen product. 

Figure 2: Flowsheet of the ASU used in the case study 

Table 1 shows the specifications that were fixed in the optimisation. All feeds to the columns enter at a pressure 

ΔP higher than the feed stage. Results of the case study were verified in Aspen Plus. 

COMPR
CWCOOLER

SPLITTER
MHEX HP

LP

THVALVE1

THVALVE2

EXPANDER

MIXER

AIR

COMPOUT

COMPAIR

LPEXP0

HPFEED0

HPFEED

LPEXP01

LPEXP
LPVD

LPBL

LPBV

LPVDOUT

LPBVOUT

LPBLOUT

HPB

LPFEED

HPD

LPREF

O2PROD

𝑃𝐿,𝑛 ≤ 𝑃𝑉,𝑛 + (1 − 𝑍𝑛)𝑀 ∀ 𝐿 ∈ 𝐿𝑖𝑞;  𝑉 ∈ 𝑉𝑎𝑝; 𝑛 ∈ 𝑁 

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Table 1: Specifications of the process 

Equipment Specification Equipment/Stream Specification 

Compressor 

(COMPR) 

Isentropic GPSA,  

Efficiency = 100 % 

Distillation Column 

(HP) 

No reboiler, total condenser (Cond) 

Feed enters at bottom-most stage 

Stage Pressure Drop, ΔP = 0.00689 bar 

Condenser duty = LP Reb Duty (ΔTmin = 1.5 °C) 

Expander 

Cooler 

(CWCOOLER) 

Isentropic GPSA,  

Efficiency = 80 % 

Outlet T = 30 °C 

Pressure Drop = 0 

Distillation Column 

(LP) 

No condenser, total reboiler (Reb) 

LPREF stream enters at top-most stage 

LPFEED and LPEXP enter on same stage 

Top stage pressure = 1.01325 bar 

Stage Pressure Drop, ΔP = 0.00689 bar 

MHEX ΔTmin = 1.5 °C Stream AIR Flow: 1 kmol/h, Pressure: 1.01325 bar, T = 25 °C 

Mol frac: 0.78 N2, 0.21 O2, 0.01 Ar 

Valves Adiabatic Stream LPEXP01 Saturated vapor at dew point 

Compressor work and work produced by the expander are calculated using the following formula: 

𝑊 =
𝑓𝑉 . 𝑅. 𝑇𝑖𝑛. 𝛾

𝛾 − 1
. ((

𝑃𝑉 ,𝑜𝑢𝑡
𝑃𝑉 ,𝑖𝑛

)

𝛾−1
𝛾

− 1)  ∀  𝑉 ∈ 𝑉𝑎𝑝 (20) 

Where 𝛾 is the ratio of specific heat capacities, 
𝑐𝑝

𝑐𝑣
, R is the ideal gas constant and 𝜂 is the efficiency. W is 

multiplied by 𝜂 for the expander and divided by 𝜂 for the compressor. Expander work will be negative. 

The flowsheet optimisation is shown below, with the objective function to minimize energy consumption per unit 

mass of O2 product. MW is the molecular weight while f(x) and g(x) are the equality and inequality constraints. 

𝑚𝑖𝑛 𝑂𝑏𝑗 =
𝑊𝐶𝑂𝑀𝑃𝑅+𝑊𝐸𝑋𝑃𝐴𝑁𝐷𝐸𝑅

∑ 𝑓𝑂2𝑃𝑅𝑂𝐷𝑦𝑖,𝑂2𝑃𝑅𝑂𝐷𝑀𝑊𝑖𝑖
+  ∑ 𝜀𝑛𝑛   s.t.  𝑓(𝑥) = 0, 𝑔(𝑥) ≤ 0 (21) 

3. Results and discussion

The performance of the novel NLP distillation model will be discussed with regard to its speed and optimisation 

results. Process parameters and objective values from the case study will also be shown and analysed.  

3.1 Performance of the novel NLP distillation model 

The case study was implemented in GAMS 24.7 and solved as an NLP model using CONOPT. As predicted, 

values of Zn were either 0 or 1 when the final optimisation was performed with the pressure drop constraints. 

Table 2 shows a comparison of model attributes and solving time for different numbers of available stages. 

Table 2: Model attributes and solving time of the NLP model 

O2 purity (mol %) Available stages Active stages Variables Equations Time elapsed (min) 

94 35 22 2,161 25,260 6 

97 100 34 5,466 154,507 20 

The NLP model generates solutions quickly as seen in Table 2, which makes it suited for multi-start initialisation 

to obtain multiple local optimal solutions or to provide good initial values and bounds to a global solver.  

Initialisation of stream properties was done by fixing parameters such as the reflux ratio and feed temperature 

of the HP column, before solving the model by minimizing the sum of the slack variable. These fixed values 

were subsequently allowed to vary. Constraints such as condenser and reboiler coupling were added prior to 

optimising the system with the objective function in Eq(21) without pressure drop before the final optimisation 

was performed with pressure drop considered. Results from the system without pressure drop tends to activate 

excess stages. When pressure drop is considered, the NLP model reduced the number of stages, showing that 

it can optimise the number of stages to an extent. However, the solutions presented here were achieved by 

optimising the system again with addition or removal of stages to compare the values of the objective function. 

Better solutions were found but the values only differed by around 1 %. The model may benefit from using 

aggregate distillation models with pressure drop considerations for initialisation, as pressure drop has an impact 

on the solution. Even with the crude initialisation procedure used here where the final values differed greatly 

from the initial values, the NLP model converged most of the time. 

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3.2 Results of the Case Study 

Table 3 shows the optimised process parameters and objective values of the case studies at different O2 product 

purities. The molar flowrates of LPBL, LPBV and LPVD add up to the molar flowrate of the AIR stream. 

Table 3: Process parameters and results of the case study 

O2

PROD 

Obj O2  

Recovery  

Stages 

HP   LP   St. No. 

HPFEED 

f T P 

HPD 

f 

Cond 

P 

LPEXP 

P 

LPBL 

f 

LPBV 

f 

mol % kJ kg-1 % No. No.  LPFeed kmol h-1 °C bar kmol h-1 bar bar kmol h-1 

94 602 95.3 7 15 8 0.883 -178 4.13 0.370 4.08 1.07 0.213 0 

95 619 96.7 8 16 7 0.786 -176 4.40 0.408 4.34 1.06 0 0.214 

96 633 96.9 10 18 8 0.787 -176 4.46 0.414 4.39 1.07 0 0.212 

97 663 97.0 12 22 13 0.836 -176 4.61 0.437 4.52 1.10 0 0.210 

98 713 93.8 12 26 16 0.943 -175 4.66 0.515 4.58 1.12 0 0.201 

In certain cases, the optimisation procedure reduced the energy consumption by 5.4 % from an initially feasible 

solution (e.g. 754) to the final value (e.g. 713), showing that the model can identify potential energy savings. A 

transition in a process parameter is seen in Table 3, where liquid product is preferred at 94 mol % purity, but 

vapour is preferred above 95 mol %. Higher reboiler and condenser duty may be needed to achieve higher O2 

and N2 purities, leading to more vapour in the LP column. At lower purities, drawing liquid may be preferred as 

the temperature of liquid is lower than vapour of the same O2 purity. A lower HP condenser pressure is then 

needed to meet the ΔTmin, since the HP distillate temperature needed to heat the reboiler is lower. The minimum 

energy requirement does not occur at maximum number of stages or 100 % O2 recovery, possibly because 

more stages and higher recovery lead to higher pressure drop throughout the columns and higher compressor 

power. The O2 recovery decreases for 98 % purity, which may be due to limitations of the ASU configuration 

presented, as the ΔT in the MHEX is at the minimum for all streams for this purity. 

4. Conclusions

A novel NLP distillation formulation was presented and implemented with a case study on an ASU. The NLP 

formulation was found to be fast with good convergence qualities when combined with Heat Integration models, 

even with crude initialisation methods. However, it tended to get stuck at local optimums and may benefit from 

better initialisation methods. Results of the case study found that 5.4 % energy savings are attainable compared 

to a feasible initial point. It was also intriguing that the minimum energy requirement and maximum product 

recovery do not coincide, with an average optimal product recovery of around 96 % for the proposed system.  

Acknowledgements 

The authors thank the financial support from the Hong Kong Research Grants Council (RGC-GRF 16211117). 

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