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 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 61, 2017 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Petar S Varbanov, Rongxin Su, Hon Loong Lam, Xia Liu, Jiří J Klemeš 
Copyright © 2017, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-51-8; ISSN 2283-9216 

Rigorous Design Optimisation for Combined Process of Raw 

Natural Gas Treating and CO2 Compression using Surrogate 

Models 

Kai Liu, Bingjian Zhang*, Qinglin Chen 

School of Chemical Engineering and Technology, Guangdong Engineering Technology Research Center for Petrochemical 

Energy Conservation, Sun Yat-Sen University, Guangzhou, 510275, China 

zhbingj@mail.sysu.edu.cn 

Raw natural gas treating processes remove enormous CO2 and consume a lot of energy. The CO2 can be further 

compressed for storage or utilization to promote environmental protection. For the purpose of economic design 

of the combined process of raw natural gas treating and CO2 compression, a new superstructure combining 

CO2 removing and compression processes is presented. In the superstructure, the rich solvent is not 

regenerated in the distillation column but through a series of flash separators at different operating pressures 

and temperatures. The removed CO2 with varying pressures is then compressed to meet the transportation 

pressure separately. The optimal process structure and operating conditions are determined by minimizing the 

total annual cost (TAC). To obtain a good trade-off between calculation accuracy and efficiency, a surrogate 

based optimization framework is presented to address the NLP problem. The complex unit operation models 

are represented by the Kriging surrogate models, which are built from training data generated via Aspen HYSYS. 

The surrogate models are then incorporated into the mathematical superstructure framework for optimization. 

The case study results indicate that the proposed process achieves a significant TAC decrease (9 % - 21 %).  

1. Introduction  

Natural gas is becoming more and more favourable because it's clean and environmental friendly. Raw natural 

gas often contains 4 – 50 % of CO2. The CO2 is separated from raw natural gas, and directly emits into the 

environment. To alleviate the greenhouse effect, it is essential to compress and transport the removed CO2 to 

storage reservoirs or utilization sites (Tapia et al., 2017). Unlike flue gas in post-combustion CO2 capture 

process, the pressure of raw natural gas is often lager than 1.5 MPa, while the gas mixture in power plants is 

about 0.1 MPa. The CO2 is often captured by amine solvent with high pressure in the absorption column and 

separated from the amine with low pressure in the distillation column. Svensson et al. (2004) indicated that the 

CO2 should be the liquid or supercritical/dense phase for efficient transport. The high-pressure rich solvent is 

decompressed for regeneration, while the removed low-pressure CO2 is compressed for transportation, 

therefore, it is possible to use the high pressure of raw natural gas to reduce the power requirement of CO2 

compression. 

A lot of research has been devoted to the optimal operation of the CO2 removing process. Mores et al. (2011) 

proposed an equilibrium stage mathematical model to determine the best operating conditions of the CO2 post-

combustion process. The proposed model was based on an equilibrium model which was not as rigorous as a 

rate-based model, Cho et al. (2015) proposed a simulation-based optimization strategy to optimize the 

arrangement and operating conditions of the CO2 removing process. Cho's model was more rigorous than the 

complete mathematical model because it integrated the rigorous commercial simulator into the optimization 

framework. Since the simulation calculation was less efficient than the equation-based model, the strategy 

considered only a number of possible modification.  

Recently, surrogate models have become a popular method for process optimization. Caballero and Grossmann 

(2008) presented an algorithm to use surrogate models in modular flowsheet. Cozada and Sahinidis (2014) 

introduced an automated learning surrogate models for simulation-based optimization. Quirante et al. (2015) 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1761284

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Liu K., Zhang B., Chen Q., 2017, Rigorous design optimisation for combined process of raw natural gas treating and 
co2 compression using surrogate models, Chemical Engineering Transactions, 61, 1717-1722  DOI:10.3303/CET1761284  

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proposed a framework for rigorous design of distillation columns using surrogate model. Eason and Biegler 

(2016) proposed a trust region filter method for glass box/ black box optimization and the convergence of the 

method to KKT points was proved.  

However, few researchers have studied the possibility to make full use of the high pressure of raw natural gas 

to reduce the CO2 compression energy. The aim of this paper is to present a new combined process of raw 

natural gas treating and CO2 compression to address the problem and propose a surrogate based optimization 

framework to optimize the process. The presented process consists of two major parts, the absorption column 

and the multi-stage flash and compression process, which acts like regeneration column in conventional process 

while offers more flexibility for amine regeneration. A superstructure is proposed to represent possible structures 

of the process. Kriging surrogate models are used to emulate the absorption column and the multi-stage flash 

and compression process using data generated by commercial simulator. The obtained surrogate models are 

incorporated into the mathematical superstructure for process structure and operation optimization. 

The paper is organized as follows. The proposed combined process is described first, followed by the 

superstructure of the process. Next, a description surrogate models is presented, and the surrogate based 

optimization methodology model is proposed. Finally, an application of the proposed methodology is presented. 

The results of the application are discussed before conclusions and perspectives are provided.  

2. Process superstructure and description 

To utilize the pressure energy of the raw natural gas, a combined raw natural gas treating and CO2 compression 

featured by multi-stage flash solvent regeneration process is presented. Figure 1 is the superstructure 

representing possible layouts of the process. In the superstructure, the regeneration column is replaced by the 

multi-stage flash process. There are k (k = 1, 2, 3… K) stages of flash and compression processes. Sour gas 

enters the absorption column at the bottom and exits the column from the top as sweet gas. The absorption 

column has two lean solvent feeds, one is at the top of the column denoted as Fl and the other is at the middle 

of the column denoted as Fs. The solvent inlet temperatures and operating pressure are fixed at 40 °C and 

6,000 kPa. The rich amine solvent Fr exits the absorption column and enters into the flash SEPk after heating 

in HEk, and then the liquid from the SEPk is split into three possible streams, Fnk, Flk and Fsk. Fnk goes to the 

next stage, Flk is pumped in the PPLk and mix with Flk’ from other flash processes to feed the absorption column 

at the top, and Fsk is pumped in the PPSk and mix with Fsk’ from other flash processes to feed in the middle of 

the absorbing column. The gas from the SEPk is cooled in CEk and then enters decanter DECk to remove water, 

the rest of the gas will be compressed in series compressors COMk, which consists of four compressors and 

coolers. Finally, the compressed CO2 from each stage merges denoted as CC. 

 

 

Figure 1: A process superstructure of the multi-stage CO2 removing and compression 

3.  Surrogate models  

Surrogate models are capable of constructing cheap-to-evaluate models to emulate the response of the 

expensive inexplicit black box functions. The Kriging interpolation is one of the most used surrogate models. 

The Kriging method views all the observed responses as if they are a stochastic process. The random field has 

a mean of 1 (1 is an n×1 column vector of ones) and variance σ2. The random variables are correlated with 

each other using the basis function expression  

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cor[Y(x(i)), Y(x(l))] = exp(- ∑ θj | xj
(i)

 - x
j

(l)
|
p

jk
j=1 ) (1)  

With pj often fixed at 2, the values of parameters , σ
2 and θj are estimated to maximize the likelihood of the 

obtained sample data: 

L = 
1

(2πσ2)
n 2⁄

|Ψ|1 2⁄
exp[ -

(y - 1μ)TΨ
-1

(y - 1μ)

2σ2
] (2)   

Where L is the likelihood, and Ψ is an n×n correlation matrix of all the observed data. 

The new prediction ŷ at x should also be consistent with the observed data and the estimated parameters. The 

augmented correlation matrix Ψ̃  with the addition of ŷ  is calculated to replace Ψ . With all the parameters 

constant, the likelihood function is determined by the prediction ŷ. And ŷ can calculated through maximizing the 

likelihood function. The mathematical details of the surrogate models can be found in the book by Forrester et 

al. (2008). 

The proposed process consists of two complex chemical processes, the absorption column and the separation 

and compression processes. Kriging surrogate models are used to substitute the two processes. In this way, 

the complex physical and chemical equations will be omitted and a more tractable model is obtained. In this 

study, the loss of amine and water is ignored. For the absorber column, the input variables include solvent 

(excluding absorbed gases) flow rate F (kg/s), the split ratio of the regenerated solvent z, the CO2 mole 

concentration of semi-lean solvent Cs, and the CO2 mole concentration of lean solvent Cl. The output variables 

include the purified gas CO2 mole fraction Cp, the rich solvent flow rate Fr (kg/s), the annualised capital cost of 

the absorption column Mc ($/y), and the temperature of the rich solvent Tr (°C). The surrogate model of the 

absorption column can be conceptually written as follows: 

[Cp, Cr, Mc, Tr] = Kr(F, z, Cs, Cl) (3) 

5 ≤ F ≤ 20 (4) 

0 ≤ z ≤ 1 (5) 

0 ≤ Cs ≤ 0.05 (6) 

0 ≤ Cl ≤ 0.03 (7) 

For the CO2 removing and the compression processes, the input variables include inlet rich solvent(excluding 

absorbed gases) flow rate Fr (kg/s), its CO2 concentration Cr, the flash temperature Tf (°C) and the flash 

pressure Pf (kPa). The output variables include the CO2 concentration of the outlet solvent Ct, the temperature 

of the outlet solvent Ts (°C), the operating cost Mo ($/y), and the annualised capital cost Ms ($/y). In each stage, 

the number of compressors is fixed at 4, and the compression ratios of all the compressors are equal. The 

surrogate model of the CO2 removing and the compression processes can be conceptually written as follows: 

[Ct, Tt, Mo, Ms] = Kr(Fr, Cr, Ts, Ps) (8) 

0 ≤ Fr ≤ 20 (9) 

0 ≤ Cr ≤ 0.05 (10) 

110 ≤ Ts ≤ 130 (11) 

150 ≤ Ps ≤ 900 (12) 

4. Optimisation framework  

Figure 2 shows the surrogate based optimization framework that is used to optimize the proposed process, as 

described below.  

1) In the preparation step, s (s = 1, 2, 3 … S) models will be selected to be surrogated, and the input variables 

and output variables will be identified for each model alongside their bounds.  

2) In the sampling step, a design of experiments will be conducted to obtain n pairs of initial sampling points 

Xs for surrogate model s. Latin Hypercube sampling method will be applied in this paper to make the 

sample points space-filling.  

3) In the data collection step, HYSYS is used to generate data pairs [Xs, Ys] according to the sampling. Notably, 

the normalization of the variables is necessary to avoid having large values dominate the results of the 

calculation.  

4) In the building step, the kriging surrogate models will be used to build the mapping between the input and 

output variables, Ŷs = fs(Xs) 

5) In the formulation process, the surrogate models will be integrated with the rest of the process equations 

to form an NLP model. The number of flash stages starts with k = 1. 

6) In the optimization step, the NLP model will be solved within MATLAB, the minimum TAC is TACmin,k, and 

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the optimal input and output variables for each surrogates are [xs,k
* , ŷ

s,k

*
] . Compare the Kriging model 

predicted results ŷ
k

*
 with the simulation results y

k
*  at the optimal point xk

* . If the relative error smaller than 

tolerance, go to the next step; if not, update the surrogate models with the point  [xs,k
* ,y

s,k
* ] and go back to 

step 4. 

7) For one-stage flash process, set k = k+1, and go back to step 5; for process with k (k > 1) stages of flash 

processes, compare the TACk with the TACk-1. If TACk greater than the TACk-1, end the process, the optimal 

number of flash stages will be k-1, and the minimum TAC is TACk-1; if not, set k = k+1 and go back to step 

5. 

 

Figure 2: Flowchart of the optimization framework 

5. Case study  

The raw natural gas composed of 85 % CH4, 5 % C2H6 and 15 % CO2, and the inlet pressure of the raw natural 

gas is 6,000 kPa. The specification for CO2 mole fraction in the purified natural gas is ranging from 1 % to 3 %. 

Figures 3 and 4 show the relative errors in testing points for separation and compression surrogate model and 

the absorption column surrogate model. The relative errors are all less than 3 %, which indicates the 

effectiveness of the surrogate models.  

In Figure 5, the line indicates the TAC of the CO2 removing and compression process, the dotted line indicates 

the TAC of the conventional process using distillation column to regenerate the rich amine solvent. The bars 

indicate the optimal number of stages for the new process. As illustrated, the new process has lower total annual 

cost under given conditions. When the sweet gas CO2 requirement is beyond 2.6 %, one-stage process is 

preferred, otherwise, two-stage process is favoured. 

Figure 6 is the optimal process structure with 1 % CO2 in sweet gas. The optimal number of stages is two, and 

the minimal TAC is 1.85 M USD. The feed to the middle of the absorption column is omitted. The total flow rate 

of amine solvent is 7.32 kg/s, all the lean solvent from the first stage of flash process goes to the second stage 

and finally enters the absorption column at the top. The pressure and temperature in the first flash stage is 488 

kPa and 130 °C. The pressure and temperature in the second stage is 150 kPa and 121 °C.  

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Figure 3: Relative errors in the tested points for absorption column (a: CO2 contents in sweet gas, b: CO2 
contents in rich solvent, c: capital cost for absorption column, d: temperature of rich solvent) 

 

Figure 4: Relative errors in the tested points for CO2 capture and compression process (a: CO2 content in lean 
gas, b: temperature of lean solvent, c: operating cost for flash process, d: capital cost for flash process) 

 

Figure 5: The optimal TAC and number of stages in the variety of sweet gas CO2 contents 

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Figure 6: The optimal process structure and operating conditions with 1 % CO2 in sweet gas 

6. Conclusion  

In this work, a superstructure for multi-stage CO2 removing and compression process in natural gas refining 

process is presented. To obtain a better trade-off between model accuracy and solving efficiency, a surrogate-

based optimization approach is proposed to address the problem. In addition, case study is carried out to 

optimize the process in a variety of different sweet gas purity requirements. The new process indicates 

significant TAC decrease (9 % to 21 %). In addition, the presented process can also offer flexible operation for 

natural gas refining plants when sweet gas CO2 requirement is changing. According to the calculation results, 

when the sweet gas CO2 requirement is beyond 2.6 %, one-stage process is preferred, otherwise, two-stage 

process is favoured. In summary, the proposed approach can be applied to explore novel process design and 

optimize operating parameters for complex chemical processes in an efficient way. 

Acknowledgments  

This research is supported by the National Natural Science Foundation of China (No. 21276288, 21376277), 

and the project of Guangdong Provincial Natural Science Foundation of China (No. 2015A030313112). 

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