DOI: 10.3303/CET25120088
Paper Received: 25 June 2025; Revised: 15 September 2025; Accepted: 27 September 2025
Please cite this article as: Kevin Lius A., Ng K.H., Mohd Yusoff N.H., Wan Y.K., Wong V.-L., 2025, Leveraging the P-Graph Framework for the
Optimal Synthesis of Pharmaceutical Wastewater Treatment Solutions, Chemical Engineering Transactions, 120, 523-528
DOI:10.3303/CET25120088
CHEMICAL ENGINEERING TRANSACTIONS
VOL. 120, 2025
A publication of
The Italian Association
of Chemical Engineering
Online at www.cetjournal.it
Guest Editors: Bing Shen How, Viknesh Andiappan, Denny K.S. Ng, Hon Loong Lam, Petar S. Varbanov
Copyright © 2025, AIDIC Servizi S.r.l.
ISBN 979-12-81206-21-2; ISSN 2283-9216
Leveraging the P-Graph Framework for the Optimal Synthesis
of Pharmaceutical Wastewater Treatment Solutions
Kevin L. Antona, Kian Hao Ngb, Nurul Husna Mohd Yusoffc, Yoke Kin Wanb, Voon-
Loong Wonga,*
aSchool of Energy and Chemical Engineering, Xiamen University Malaysia, Jalan Sunsuria, Bandar Sunsuria, 43900
Sepang, Selangor Darul Ehsan.
bDepartment of Chemical and Environmental Engineering, Faculty of Science and Engineering, University of Nottingham
Malaysia, 43500 Semenyih, Selangor, Malaysia.
cExxonMobil Research and Development Center, NJ 08801-3096, Clinton, New Jersey, Unites States.
voonloong.wong@xmu.edu.my
The increasing demand for pharmaceutical products has led to a rise in pharmaceutical wastewater, which
poses serious environmental and health threats due to the presence of complex contaminants including high
chemical oxygen demand (COD), biological oxygen demand (BOD), total suspended solids (TSS), heavy
metals, and residual pharmaceutical compounds. Traditional treatment systems struggle to meet regulatory
standards, especially in countries like Malaysia where stringent discharge limits are enforced under the
Environmental Quality Act 1974 - Environmental Quality (Industrial Effluent) Regulations 2009. In the present
study, a proposed methodology applies a stagewise treatment structure, from preliminary to advanced
treatment, integrating various physical, chemical, and biological technologies for the effective reduction of key
water quality parameters. A graph-theoretic method known as P-graph structure generation algorithms was
further implemented to study multiple feasible treatment pathways. Each configuration was assessed based on
pollutant removal efficiency of COD, BOD, TSS and economic viability. A case study was solved to simulate the
application of this framework, demonstrating its capability to identify optimal treatment networks that comply
with the Environment Quality Regulations 2009 while minimizing operational costs. This research highlights the
potential of P-graph modelling as a practical decision-support tool for pharmaceutical wastewater. It helps
design pharmaceutical wastewater treatment systems that are both affordable and meet environmental
regulations.
1. Introduction
The pharmaceutical market has been experiencing steady growth, driven by advancements in medical research,
population increases, and rising global healthcare demands (DrugPatentWatch, 2025). Global pharmaceutical
expenditures, excluding COVID-19 vaccine spending, are expected to reach approximately $ 1.6 T by 2025,
growing at a compound annual growth rate (CAGR) of 3 % to 6 % (Van Arnum, 2021). While this expansion
benefits healthcare outcomes, it also significantly increases the generation of pharmaceutical wastewater.
According to 2022 data from the United Nations, only 38 % of industrial wastewater in 22 countries was treated,
and merely 27 % of it was treated safely, underscoring the pressing need for effective wastewater treatment
technologies in the pharmaceutical sector (Un-Water, 2025).
Pharmaceutical wastewater contains harmful contaminants such as pharmaceutical compounds, pathogens,
and heavy metals. In Lanzhou, China, high levels of β-lactam antibiotics such as ampicillin, ceftriaxone,
amoxicillin, and cefazolin have been detected (Ji et al., 2021), while wastewater in Sungai Langat, Malaysia,
contains pollutants like paracetamol and diclofenac (Lie et al., 2024). These substances cause COD levels of
1,000–10,000 mg/L, exceeding the limits of conventional treatments (Leistner, 2023). Such pollution can harm
aquatic ecosystems by disrupting microbes, affecting fertility, and causing genetic issues (Samal et al., 2022).
523
To address the dangers of harmful contaminants in water bodies, governments, including Malaysia's, have
implemented regulations such as the Environmental Quality Act 1974, the Environmental Quality (Sewage)
Regulations 2009, the Environmental Quality (Industrial Effluent) Regulations 2009, and the Water Services
Industry (Prohibited Effluent) Regulations 2021. These set enforceable limits on effluent quality and prohibit
specific toxic discharges. Additionally, Malaysia's National Water Quality Standards (NWQS), developed by the
Department of Environment (DOE), provide a framework for assessing surface water quality. Thus, selecting
appropriate wastewater treatment technology is crucial for optimizing costs, energy use, and resource recovery
while ensuring sustainability and compliance.
This paper focuses on the development and optimization of pharmaceutical wastewater treatment systems using
the P-graph framework to comply with regulatory standards set by the National Water Quality Standards
(NWQS), the Environmental Quality Act 1974, and the Industrial Effluent Regulations 2009. While the P-graph
method has been applied in previous studies to general wastewater treatment by Yenkie et al. (2021) and
tannery wastewater by Aboagye et al. (2021), its application to pharmaceutical wastewater treatment remains
largely unexplored. Wastewater from pharmaceutical manufacturing is characterized by high levels of chemical
oxygen demand (COD), biological oxygen demand (BOD), and total suspended solids (TSS), making its
treatment particularly challenging. These high COD concentrations and fluctuating flow rates often exceed the
capabilities of standard treatment facilities. Achieving stringent COD reduction targets requires specialized
treatment systems, and the operation and management of such systems involve substantial costs. These
challenges underline the urgent need for cost-effective and efficient treatment solutions.
2. Methodology
The P-graph approach was adopted to systematically synthesize optimal configurations for pharmaceutical
wastewater treatment systems using a stage wise approach. This framework has been widely used to assess
combinatorial problems, including those in process network design (Friedler et al., 2019).P-graph framework
uses two node types: O-type nodes for technologies and M-type nodes for materials, connected by arcs
indicating flow direction. Key algorithms like Maximal Structure Generation (MSG), Solution Structure
Generation (SSG), and Accelerated Branch and Bound (ABB) generate optimal or feasible process networks
while estimating costs (Friedler et al., 2022). P-graph able to present all feasible solutions ranked by cost, unlike
conventional optimization methods, making it ideal for designing or retrofitting wastewater treatment systems.
The advantage of the P-graph approach over other methods is its ability to provide a clear and visual
representation of process networks using bipartite graphs, making it easier to understand, communicate, and
modify process structures (Benjamin et al., 2021).
2.1 Stagewise Structure of Pharmaceutical Wastewater Treatment
This study uses a six-stage system: preliminary, primary, secondary, tertiary, and advanced treatments. Each
stage targets specific pollutants, starting from large solids to produce reusable effluent (i.e., treated water from
the final treatment) and supporting efficient, low-energy operations. The treatment structure is summarized in
Figure 1.
Figure 1: Stage wise structure of pharmaceutical wastewater treatment used in this project with its abbreviation.
The wastewater first enters preliminary treatment to remove particulate solids, followed by primary treatment to
further remove dissolved solids as well as some COD and BOD. Next, the treated wastewater undergoes
biological treatment, which focuses on the removal of COD and BOD. After that, the water proceeds to tertiary
or polishing treatment to ensure that the concentrations of TSS, BOD, and COD meet the discharge limits. In
524
addition, this study explores alternative bypass options in the advanced and final treatment stages, allowing the
treated wastewater from the tertiary stage to bypass the advanced or final treatments (or both) depending on
the desired water quality to be achieved by the treatment plant. If higher-quality water is required, such as
ensuring the absence of pathogens, Fenton oxidation and UV light treatments will be necessary. Otherwise, the
water quality produced from the tertiary treatment is sufficient. The selection of technologies, their placement
within the treatment sequence, associated costs, and removal efficiencies used in this study are all based on
data obtained from relevant literature sources (see Supplementary).
2.2 Case study
This project targets the removal of COD, BOD, and TSS, with influent data sourced from a pharmaceutical
industry, as shown in Table 1. Effluent targets follow Malaysia’s NWQS and the Environmental Quality Act 1974
– Industrial Effluent Regulations 2009. The aims to meet Class I water standards: BOD ≤ 1 mg/L, COD ≤ 10
mg/L, and TSS ≤ 25 mg/L. These standards indicate very low pollution levels, suitable for ecological protection
(Kawan et al., 2022). The objective of this project is to minimize the total cost by using the P-graph framework,
with decision variables including the selection of treatment technologies and the combination and sequence of
various treatment stages. This project assumes that the initial and final flow rates remain constant, as the focus
is on reducing pollutant mass flowrate while maintaining a steady water within the treatment system.
Table 1: The influence of pharmaceutical wastewater and final product requirement.
Parameter Value of Inlet Value of Final Product
Flow rate (m3/day) 200 200
COD (mg/L) 650 <10
BOD (mg/L) 330 <1
TSS (mg/L) 90 <25
As previously mentioned, the removal efficiency for each treatment stage was determined based on reported
values (see Supplementary). After establishing these efficiencies and verifying that each stage could meet the
required discharge standards, the next step was to calculate the number of pollutants removed at each stage.
This calculation was carried out using the formula developed in this study, as shown Eq(1) where 𝑝𝑓(𝑛−1) is
mass flowrate of pollutants in previous stage n-1:
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑝 (𝑝𝑜𝑙𝑙𝑢𝑡𝑎𝑛𝑡) 𝑟𝑒𝑚𝑜𝑣𝑒𝑑, 𝑅𝑝 = 𝑅𝑒𝑚𝑜𝑣𝑎𝑙 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑥 𝑝𝑓(𝑛−1) (1)
Consequently, the mass flow rate of pollutants entering the next stage can be calculated using Eq(2), where
𝑝𝑓(𝑛+1) is the total mass flowrate of pollutant for stage n+1.
𝑝𝑓(𝑛+1) = 𝑝𝑓(𝑛−1) − 𝑅𝑝 (2)
The cost estimation model in this study is based on literature data (see Supplementary) and assumes a linear
relationship between equipment cost and capacity. As shown in Eq(3), the equipment cost (Ci) is calculated as
a function of its capacity (Qi). Here, Q1 and C1 are values from the literature, while Q2 represents the design
capacity used in this study (200 m³/day).
𝐶2 = 𝐶1 ∗
𝑄2
𝑄1
(3)
The P-graph structure used in this study is shown in Figure 2. Raw water input was calculated by multiplying
pollutant concentrations (COD, BOD, TSS) by a flow rate of 200 m³/day, resulting in a total mass flow rate of
about 214 kg/day. Cost inputs were based on prior estimates, while removal efficiencies were excluded to
maintain a steady-state flow and avoid skewing cost results. The final product was defined by minimum pollutant
limits, and treated water was based on the mass of pollutants removed. The payout period used in this
optimization was 10 years, which is the default setting in the P-graph framework.
3. Results and Discussion
In this project, the Accelerated Branch and Bound (ABB) algorithm was used to generate 192 feasible treatment
network solutions ranked by cost, supporting more informed decision-making across multiple optimal
configurations. While the ABB algorithm was used to generate feasible treatment network structures based on
cost and connectivity, the pollutant discharge limits (COD, BOD, TSS) were treated as final product assumptions
525
and manually validated in Excel. This manual validation was necessary because including removal efficiencies
at each treatment stage would alter the raw material flow rate and affect cost calculations, whereas this study
maintained a fixed flow rate of 200 m³/day. The top five cost-effective solutions are presented in Table 2. Unlike
conventional methods, the P- graph approach offers a variety of feasible pathways, allowing engineers to
explore different combinations of treatment technologies, such as with or without UV disinfection, to select the
most suitable configuration.
Figure 2: The superstructure configuration of P-graph that used
The P-graph superstructure was constructed into a stagewise sequence. At each stage, multiple competing
technologies (such as SBR, ASP, and MBR in the primary stage) are embedded in parallel. Rigorous Excel
calculations confirmed that bypassing any of the preliminary through tertiary stages would cause effluent quality
to breach Malaysia’s COD, BOD, and TSS limits, so only the advanced and final stages were permitted full
bypass options.
Table 2: Five optimal structures that identified using Accelerated Branch and Bound (ABB) Algorithm.
Rank Operating Units Total Cost ($/day) Investment Cost ($)
#1 Screen, chemical coagulation and clarifier, activated sludge,
clarifier, activated carbon filtration
438.28 185,954.28
#2 Screen, chemical coagulation and dissolved air flotation,
activated sludge, clarifier, activated carbon filtration
443.12 190,056.57
#3 Sedimentation tank, chemical coagulation and clarifier,
activated sludge, clarifier activated carbon filtration
448.04 224,361.66
#4 Sedimentation tank, chemical coagulation and air flotation,
activated sludge, clarifier, activated carbon filtration
452.87 228,463.95
#5 Screen, chemical coagulation and clarifier, activated sludge,
clarifier, activated carbon filtration, UV light
453.38 187,004.64
526
3.1 Economic Evaluation
Based on the analysis conducted using the P-graph algorithm, it was found that among the top five solutions,
the most expensive structure incurred a total operating cost of 453.38 $/d, equivalent to approximately 2.27 $/m3
of treated wastewater. In comparison, the first-ranked solution had a daily operating cost of about $ 438.28, or
roughly 2.19 $/m3. This indicates that the fifth-ranked structure is only around 3.33 % more expensive than the
first-ranked one, reflecting a relatively small cost difference among the top five solutions. Additionally, the cost
gap between the first- and second-ranked structures is just 2.5 %, further demonstrating that the P-graph
algorithm effectively generates a well-ranked set of feasible solutions with minimal cost variation. Among these
solutions, rank #1 emerged as the most economically advantageous in terms of investment cost, requiring the
lowest total investment of $ 185,954.28. This configuration consists of a combination of screen, chemical
coagulation and clarifier, activated sludge, clarifier, and activated carbon filtration. On the other hand, rank #5
is particularly suitable for situations where the wastewater contains a high concentration of bacteria or viruses,
as it includes an additional UV disinfection stage. With an operating cost of approximately 453.38 $/d (or about
2.27 $/m3) and an investment cost of around $ 187,004.64, it offers a balanced option between performance
and overall cost. The availability of the fifth-ranked structure as a feasible solution provides engineers with
flexibility, allowing them to select a design that best fits their specific treatment needs, particularly when
addressing high levels of microbial contamination.
3.2 Performance Evaluation
As can be seen in Table 3, all feasible structures meet the National Water Quality Index of Malaysia standards
(COD < 10 mg/L, BOD < 1 mg/L, TSS < 25 mg/L). Structures ranked #1, #2, and #5 yield identical final
concentrations. This outcome is attributed to two main factors. First, the project focuses solely on COD, BOD,
and TSS, and the differences among the feasible solutions primarily involve the addition of UV light, which does
not significantly affect these parameters. Second, the variations lie in the sludge settling methods used after
chemical coagulation (either through dissolved air flotation or clarifier systems) which also do not significantly
impact the final concentrations of the targeted pollutants. Structures #3 and #4 also produce the same results
for similar reasons. The main difference across structures lies in TSS removal efficiency sedimentation tanks
perform better, achieving a lower final TSS concentration (0.0057 mg/L) compared to screens (0.037 mg/L).
Table 3: Concentration of removed and remaining pollutants for the five best optimal structures under the cost
minimization objective.
Rank Pollutant
Concentration Removed (mg/L) Concentration Remain (mg/L)
SC CFC
AS +
Clarifier
ACF
UV
Light
SC CFC
AS +
Clarifier
ACF UV Light
#1
COD 0 624 23.4 1.85
-
650 26 2.6 0.75
- BOD 0 184.8 143.98 1.149 330 145.2 1.22 0.071
TSS 31.5 53.82 4.633 0.01 58.5 4.68 0.047 0.037
Pollutant SC CFD
AS +
Clarifier
ACF
UV
Light
SC CFD
AS +
Clarifier
ACF UV Light
#2
COD 0 624 23.4 1.85
-
650 26 2.6 0.75
- BOD 0 184.8 143.98 1.149 330 145.2 1.22 0.071
TSS 31.5 53.82 4.633 0.01 58.5 4.68 0.047 0.037
Pollutant ST CFC
AS +
Clarifier
ACF
UV
Light
ST CFC
AS +
Clarifier
ACF UV Light
#3
COD 0 624 23.4 1.85
-
650 26 2.6 0.75
- BOD 0 184.8 143.98 1.149 330 145.2 1.219 0.071
TSS 81 8.28 0.7128 0.0015 9 0.72 0.0072 0.0057
Pollutant ST CFD
AS +
Clarifier
ACF
UV
Light
ST CFD
AS +
Clarifier
ACF UV Light
#4
COD 0 624 23.4 1.85
-
650 26 2.6 0.75
- BOD 0 184.8 143.98 1.149 330 145.2 1.219 0.071
TSS 81 8.28 0.7128 0.0015 9 0.72 0.0072 0.0057
Pollutant SC CFC AS +
Clarifier
ACF UV
Light
SC CFD AS +
Clarifier
ACF UV Light
#5
COD 0 624 23.4 1.85 1.85 650 26 2.6 0.75 0.75
BOD 0 184.8 143.98 1.149 1.149 330 145.2 1.22 0.071 0.071
TSS 31.5 53.82 4.633 0.01 0.01 58.5 4.68 0.047 0.037 0.037
527
4. Conclusions
This study demonstrates the effectiveness of the P-graph framework in designing optimal pharmaceutical
wastewater treatment systems. By analysing 192 feasible structures, the top five were selected based on cost
and compliance with Malaysia’s environmental standards. The best configuration combined screening, chemical
coagulation, activated sludge, and activated carbon filtration. While the study focused on COD, BOD, and TSS,
future work should include other contaminants, validate results at scale, and integrate dynamic models with non-
linear optimization. Incorporating pollutant thresholds directly into the model will also help minimize over-
treatment and better utilize partial bypass options for improved cost-efficiency.
Acknowledgments
This work was financially supported by Xiamen University Malaysia Research Fund (XMUMRF) (Grant no.
XMUMRF/2025-C15/IENG/0078).
The data used for this P-graph optimization can be found in the Supplementary Document
(drive.google.com/file/d/1XWzzFbKoMyy3-O04INuju9ZEWtbJsSEy/view).
References
Aboagye E.A., Pimentel J., Orosz Á., Cabezas H., Friedler F., Yenkie K.M., 2021, Efficient Design and
Sustainability Assessment of Wastewater Treatment Networks using the P-graph Approach: A Tannery
Waste Case Study. Chemical Engineering Transactions, 88, 493-498.
Basso S., 2023, The four stages of wastewater treatment plants – IDRICA accessed 02.06.2025
DrugPatentWatch, 2025, The Influence of Emerging Markets on the Pharmaceutical Industry - DrugPatentWatch
– Transform Data into Market Domination. DrugPatentWatch – Transform Data Into Market Domination
accessed 10.06.2025
Frankel T., 2025, What Is Tertiary Wastewater Treatment, and How Does It Work? SSI Aeration
accessed 20.06.2025
Friedler F., Aviso K.B., Bertok B., Foo D.C., Tan R.R., 2019, Prospects and challenges for chemical process
synthesis with P-graph. Current Opinion in Chemical Engineering, 26, 58–64.
Friedler F., Orosz Á., Losada J.P., 2022, P-Graphs for Process Systems engineering: Mathematical Models and
Algorithms. Springer Nature.
Ji J., Gao T., Salama E., El-Dalatony M.M., Peng L., Gong Y., Liu P., Li X., 2021, Using Aspergillus niger whole-
cell biocatalyst mycelial aerobic granular sludge to treat pharmaceutical wastewater containing β-lactam
antibiotics. Chemical Engineering Journal, 412, 128665.
Kawan J.A., Suja F., Pramanik S.K., Yusof A., Rahman R.A., Hasan H.A., 2022, Effect of Hydraulic Retention
Time on the Performance of a Compact Moving Bed Biofilm Reactor for Effluent Polishing of Treated
Sewage. Water, 14(1), 81.
Leistner T., 2023, Pharmaceutical wastewater treatment. clearfox.com. accessed 10.06.2025
Lie M., Rubiyatno N., Binhudayb F.S., Thao N.T.T., Kristanti R.A., 2024, Assessing the Impact of Pharmaceutical
Contamination in Malaysian Groundwater: Risks, Modelling, and Remediation Strategies. Tropical Aquatic
and Soil Pollution, 4(1), 43–59.
Nathanson A,J., Ambulkar, Archis, 2025, Wastewater treatment | Process, History, Importance, Systems, &
Technologies. Encyclopedia Britannica accessed 02.06.2025
Samal K., Mahapatra S., Ali M.H., 2022, Pharmaceutical wastewater as Emerging Contaminants (EC):
Treatment technologies, impact on environment and human health. Energy Nexus, 6, 100076.
Un-Water, 2025, Progress on Wastewater Treatment – 2024 Update | UN-Water. UN-Water
accessed 01.06.2025
Van Arnum P., 2021, The Global Bio/Pharma Market: Where’s the Growth? - DCAT Value Chain Insights. DCAT
Value Chain Insights
accessed 01.06.2025
Yenkie K.M., Pimentel J., Orosz Á., Cabezas H., Friedler F., 2021, The P‐graph approach for systematic
synthesis of wastewater treatment networks. AIChE Journal, 67(7), e17253.
Benjamin M.F., Aviso K., Belmonte B.A., Tan R.R., 2021, Optimal operations of a bioenergy park under capacity
disruptions via the P-graph method. Chemical Engineering Transactions, 89, 139-144.
528
0260.pdf
Leveraging the P-Graph Framework for the Optimal Synthesis of Pharmaceutical Wastewater Treatment Solutions