001.docx
CHEMICAL ENGINEERING TRANSACTIONS
VOL. 83, 2021
A publication of
The Italian Association
of Chemical Engineering
Online at www.cetjournal.it
Guest Editors: Jeng Shiun Lim, Nor Alafiza Yunus, Jiří Jaromír Klemeš
Copyright © 2021, AIDIC Servizi S.r.l.
ISBN 978-88-95608-81-5; ISSN 2283-9216
Mathematical Optimisation of Biogas Production and
Utilisation
Aminullah Mohtara, Anbukarasi Ravia, Wai Shin Hoa,*, Chee Wan Choya, Haslenda
Hashima, Zarina Ab Muisa, Nor Alafiza Yunusa, Mimi Haryani Hassimb, Angel Xin
Yee Maha
aProcess Systems Engineering Centre (PROSPECT), School of Chemical and Energy Engineering, Faculty of Engineering,
Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia
bSchool of Chemical and Energy Engineering, Faculty of Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor,
Malaysia
hwshin@utm.my
Palm oil mill effluent (POME) is a source of biogas generation that can be a substitute for fossil fuel. High
content of biological oxygen demand (BOD) and chemical oxygen demand (COD) of POME has the
advantage to produce large amount of biogas through anaerobic digestion. The purpose of this research is to
develop a mathematical model to determine the optimal process pathway of biogas, covering from the
purification technology to mode of transportation and utilization. A hypothetical case study is conducted to run
and test the model, in which different target location with different utilization mode was chosen. The model
chose membrane separation of biogas, pipeline transportation to the targeted site, and electricity generation
as the optimal pathway for biogas processing and utilization. Sensitivity analysis is performed to determine the
impact of product price on the biogas process pathway selection. The sensitivity analysis revealed that the
price of Bio-CNG has an impact on the model. Sensitivity analysis suggested the Bio-CNG sales price should
be at least 10.4 USD/GJ to be economically feasible.
1. Introduction
Malaysia has shown good commitment to utilizing renewable energy. One of the major steps taken is to utilize
oil palm biomass. It is expected that crude palm oil (CPO) is able to produce 1.95 × 107 t and possibly produce
5.85 × 107 m3 of Palm Oil Mill Effluent (POME) waste yearly (MPOB, 2016). POME is a liquid effluent which is
high in biological oxygen demand (BOD). Through anaerobic breakdown, it could produce up to 1.04 × 109 m3
of biogas and generate 4.38 TWh/y of power (expecting 40 % gas engine productivity). POME has to be
anaerobically digested to produce biogas and purified to remove unwanted gases such as hydrogen sulfide
(H2S), moisture, and carbon dioxide (CO2) before it can be considered for utilization as fuel for power
generation, as compressed natural gas (bio-CNG) or as liquefied natural gas (bio-LNG). The processed
biogas is then transported to other points of utilization as palm oil mills are often located far away, estimated to
be more than 10 km away from nearby towns. These factors lead to additional investment cost that prevents
the investor from investing in biogas projects from POME for offsite utilization (Mohtar et al., 2017).
According to Figure 1, several purification technologies are available such as water scrubber, PSA, membrane
separation, chemical absorption, and physical absorption. After purification, biogas is compressed for
transportation. The final pressure of compression is dependent on the mode of transportation, either via truck
(after bottling) or through pipeline. Options of biogas utilization include electricity generation and as bio-CNG
for various application such as industrial heating, cooking, and fuel for natural gas vehicles. This study aims to
develop a mathematical model to identify the optimal solution for purifying, transporting and utilizing biogas
from POME for maximum profit.
Over the years, many studies have been done on biogas system optimization that deals with the mode of
transportation, utilization, and demand. To optimize the production and investment plan for a biogas supply
chain, a mathematical model was developed by Jensen et al. (2017) considering the mass and energy losses.
DOI: 10.3303/CET2183075
Paper Received: 15/07/2020; Revised: 26/10/2020; Accepted: 01/11/2020
Please cite this article as: Mohtar A., Ravi A., Ho W.S., Choy C.W., Hashim H., Ab Muis Z., Yunus N.A., Hassim M.H., Mah A.X.Y., 2021,
Mathematical Optimisation of Biogas Production and Utilisation, Chemical Engineering Transactions, 83, 445-450 DOI:10.3303/CET2183075
445
Egieya et al. (2019) presented a generic mixed-integer linear programming (MILP) model for optimizing biogas
supply network to generate electricity over monthly periods by maximizing profit. Another study developed a
mathematical model to decide the locations for biogas plant, types and quantities of feedstock and products,
size of land area for growing biomass, capacities of conversion technologies, inventories of feedstock and
products, transportation modes and logistics (Zirngast et al., 2019). Galvez et al. (2015) proposed a
mathematical model for reverse logistics and to optimize a proposed logistic network, ensuring the lowest cost
and the shortest possible travelling distance. Díaz-Trujillo and Nápoles-Rivera (2019) presented a multi-
objective optimization approach for biogas supply chain based on a superstructure to satisfy the biogas and
bio-fertilizer demand in a Mexico region at the maximum profit and the minimum environmental impact. Sarker
et al. (2019) formulated a mixed-integer non-linear programming (MINLP) model to optimally locate the
feedstock collection hubs and bio-methane gas plants for minimum cost of operation.
Although many studies have been done on the biogas supply chain with nearby energy demands, none of
these studies considers purification technology in the mathematical model. In this study, a mixed-integer linear
programming (MILP) model is developed to include the selection of purification technology in biogas supply
chain models. Further analysis is conducted to identify the Bio-CNG price to make biogas project from POME
attractive for offsite utilization.
Figure 1: Superstructure of biogas process pathway
2. Mathematical formulation
This section describes the methodology of the work, which involves the formulation of mathematical model for
optimization study. An optimization model contains an objective function, equality constraints and inequality
constraints.
As mentioned in the introduction, the objective of this research is to identify the optimal pathway to utilize
biogas generated from POME anaerobic digestion for maximum profit. The model presented is a MILP model.
Eq(1) describes the objective of the model, which is to maximize the profit, z by subtracting the total cost
(including compressor, transportation and purification cost), Totalcost from the sales revenue of biogas,
Salesprice for different type utilization (electricity or bio-CNG).
𝑚𝑚𝑚𝑚𝑚𝑚 𝑧𝑧 = 𝑆𝑆𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝑇𝑇𝑇𝑇𝑇𝑇𝑚𝑚𝑆𝑆𝑆𝑆𝑇𝑇𝑆𝑆𝑇𝑇 (1)
Several technologies for biogas purification are considered in this study. Eq(2) and Eq(3) are used to calculate
the capital expenditure, PTiCAPEX (USD/y) and operation expenditure, PTiOPEX (USD/y) of purification
technology. The biogas that has been purified is called biomethane. The capital expenditure is calculated by
multiplying the equipment price, PTiSP (USD/m3/h) with biomethane processed, Fi (m3/h). The operating
expenditure is obtained by multiplying the unit operating and maintenance price of the purification technology,
O&MPri (USD/kWh) with the energy consumption during each purification process, EConPTi (kWh/m3) and
biomethane processed, where LT is the number of operating hours in a year.
𝑃𝑃𝑇𝑇𝑖𝑖𝐶𝐶𝐶𝐶𝑃𝑃𝐶𝐶𝐶𝐶 = 𝑃𝑃𝑇𝑇𝑖𝑖 𝑆𝑆𝑃𝑃 × 𝐹𝐹𝑖𝑖 (2)
𝑃𝑃𝑇𝑇𝑖𝑖𝑂𝑂𝑃𝑃𝐶𝐶𝐶𝐶 = (𝑂𝑂&𝑀𝑀𝑃𝑃𝑆𝑆 𝑖𝑖 × 𝐶𝐶𝐶𝐶𝑇𝑇𝑛𝑛𝑃𝑃𝑃𝑃𝑖𝑖 × 𝐹𝐹𝑖𝑖) × 𝐿𝐿𝑇𝑇 (3)
446
The cost of compression is calculated using Eq(4) to Eq(8). The compressor price is obtained from a graphical
correlation retrieved from Loh et al. (2002). Since the biomethane transported via pipeline and truck requires
different pressure, the calculation of compressor cost is demonstrated using the biomethane with truck
transportation, while the same procedure can be applied for pipeline transportation. The capital expenditure of
compressor, Compressor CAPEX (USD/y) can be calculated using the purchase price of compressor,
Compressorj PurP (USD/m3/h) and amount of biomethane after purification technology, BioVT (m3/h) as shown
in Eq(4).
The operating cost of compressor, Compressor OPEX (USD/y) is calculated as shown in Eq(5). The operating
cost is obtained by dividing energy consumption, Econ (kWh/h) and electric tariff, tariff (USD/kWh) by motor
efficiency (%) and multiply with the total operating hours in a year. In this equation, it is assumed that the
motor efficiency of the compressor is 95 %. Eq(6) presents the calculation for compressor adiabatic head,
HAD,T (lbf/lbm), where R is the gas constant obtained by 1544 divided with the molecular weight of biomethane,
T1 is the inlet temperature in deg R, K is the specific heat ratio, P1 is the inlet pressure in psia and P2,T is the
pressure required for truck transportation in psia. Eq(7) converts the inlet flowrate from m3/h to lb/min, where
ρCH4 (kg/m3) is the density of biomethane. In Eq(8), the compressor power consumption is determined, where
EA is the adiabatic efficiency of the compressor.
𝐶𝐶𝑇𝑇𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑇𝑇𝑆𝑆 𝐶𝐶𝐶𝐶𝑃𝑃𝐶𝐶𝐶𝐶 = 𝐶𝐶𝑇𝑇𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑇𝑇𝑆𝑆𝑗𝑗 𝑃𝑃𝑃𝑃𝑆𝑆𝑃𝑃 × 𝐵𝐵𝑆𝑆𝑇𝑇𝑉𝑉𝑃𝑃 (4)
𝐶𝐶𝑇𝑇𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑇𝑇𝑆𝑆 𝑂𝑂𝑃𝑃𝐶𝐶𝐶𝐶 = 𝐸𝐸𝐸𝐸𝐸𝐸𝑛𝑛𝑇𝑇 × 𝑡𝑡𝑡𝑡𝑡𝑡𝑖𝑖𝑡𝑡𝑡𝑡
m𝐸𝐸𝑡𝑡𝐸𝐸𝑡𝑡 𝑒𝑒𝑡𝑡𝑡𝑡𝑖𝑖𝑒𝑒𝑖𝑖𝑒𝑒𝑛𝑛𝑒𝑒𝑒𝑒
× 𝐿𝐿𝑇𝑇 (5)
𝐻𝐻𝐴𝐴𝐴𝐴,𝑃𝑃 =
𝑅𝑅𝑇𝑇1
(𝐾𝐾 − 1)/𝐾𝐾
��
𝑃𝑃2,𝑃𝑃
𝑃𝑃1
�
(𝐾𝐾−1)/𝐾𝐾
− 1� (6)
𝑊𝑊𝑃𝑃 = 𝐵𝐵𝑆𝑆𝑇𝑇𝑉𝑉𝑃𝑃 × 𝜌𝜌𝐸𝐸𝐶𝐶4 × 0.0367437 (7)
𝐶𝐶𝐶𝐶𝑇𝑇𝑛𝑛𝑃𝑃 =
𝑊𝑊𝑃𝑃𝐻𝐻𝐴𝐴𝐴𝐴,𝑃𝑃
33000 𝐶𝐶𝐴𝐴 × 1.3405
(8)
In this study, two modes of biogas transportation are considered, which is transportation using the natural gas
pipeline or via truck transportation. Eq(9) is the general equation for pipeline transportation cost,
Transportation CostP (USD/y), where PriceP (USD/MMBtu) is the unit pipeline cost and EBioAck (MMBtu/h) is
the energy content of biomethane stream. In Eq(10), the energy content of biomethane was calculated using
the heating value of biomethane, HVCH4 (MJ/kg), biomethane flowrate in pipeline, BioVP (m3/h), and density of
biomethane, ρCH4 (kg/m3).
𝑇𝑇𝑆𝑆𝑚𝑚𝑛𝑛𝑆𝑆𝑆𝑆𝑇𝑇𝑆𝑆𝑇𝑇𝑚𝑚𝑇𝑇𝑆𝑆𝑇𝑇𝑛𝑛 𝐶𝐶𝑇𝑇𝑆𝑆𝑇𝑇𝑃𝑃 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑃𝑃 × 𝐶𝐶𝐵𝐵𝑆𝑆𝑇𝑇𝐴𝐴𝐸𝐸𝐴𝐴 × 𝐿𝐿𝑇𝑇 (9)
𝐶𝐶𝐵𝐵𝑆𝑆𝑇𝑇𝐴𝐴𝐸𝐸𝐴𝐴 =
𝐻𝐻𝑉𝑉𝐸𝐸𝐶𝐶4 × 𝐵𝐵𝑆𝑆𝑇𝑇𝑉𝑉𝑃𝑃 × 𝜌𝜌𝐸𝐸𝐶𝐶4
1055.87
(10)
The transportation of biogas in truck is dependent on the volume of biogas, BioVT (m3) after compression
process. The volume of biogas after compression, CompBioVT (m3/h) is determined using Eq(11). The number
of trip required in a day, Number of Trip is identified using Eq(12) by dividing volume of biogas produced in a
day by truck capacity, Truckcapacity (m3/truck). OPT represents the number of hours the plant is operating in a
day. The time required per trip can be calculated using Eq(13), where Distance represents the transportation
distance and Truck Speed is the mean travelling speed of the truck. The time lag represents time required for
loading and unloading of products. Eq(14) computes the number of truck required where the time available
represents the time available for transportation per truck per day.
The total cost for the truck purchase, TrCostT (USD/y) can be calculated using Eq(15) where the total number
of trucks is multiplied with the price per truck, TrPriceT (USD/truck). Eq(16) is used to calculate the operation
and maintenance cost of truck delivery, TrO&MT (USD/y), where O&MPriceT (USD/km) is the unit operating
and maintenance cost per km travelled and OPD is the days of operation in a year.
𝐶𝐶𝑇𝑇𝑚𝑚𝑆𝑆𝐵𝐵𝑆𝑆𝑇𝑇𝑉𝑉𝑃𝑃 = 𝐵𝐵𝑆𝑆𝑇𝑇𝑉𝑉𝑃𝑃
𝑃𝑃1
𝑃𝑃2,𝑃𝑃
(11)
𝑁𝑁𝑃𝑃𝑚𝑚𝑁𝑁𝑆𝑆𝑆𝑆 𝑇𝑇𝑜𝑜 𝑇𝑇𝑆𝑆𝑆𝑆𝑆𝑆 =
𝐶𝐶𝑇𝑇𝑚𝑚𝑆𝑆𝐵𝐵𝑆𝑆𝑇𝑇𝑉𝑉𝑃𝑃 × 𝑂𝑂𝑃𝑃𝑇𝑇
𝑇𝑇𝑆𝑆𝑃𝑃𝑆𝑆𝑇𝑇𝑒𝑒𝑡𝑡𝑐𝑐𝑡𝑡𝑒𝑒𝑖𝑖𝑡𝑡𝑒𝑒
(12)
447
𝑇𝑇𝑆𝑆𝑚𝑚𝑆𝑆 𝑆𝑆𝑆𝑆𝑟𝑟𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟 𝑆𝑆𝑆𝑆𝑆𝑆 𝑇𝑇𝑆𝑆𝑆𝑆𝑆𝑆 =
𝑁𝑁𝑃𝑃𝑚𝑚𝑁𝑁𝑆𝑆𝑆𝑆 𝑇𝑇𝑜𝑜 𝑇𝑇𝑆𝑆𝑆𝑆𝑆𝑆 × 2 × 𝐷𝐷𝑆𝑆𝑆𝑆𝑇𝑇𝑚𝑚𝑛𝑛𝑆𝑆𝑆𝑆
𝑇𝑇𝑆𝑆𝑃𝑃𝑆𝑆𝑇𝑇 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟
+ 𝑇𝑇𝑆𝑆𝑚𝑚𝑆𝑆 𝐿𝐿𝑚𝑚𝐿𝐿 (13)
𝑁𝑁𝑃𝑃𝑚𝑚𝑁𝑁𝑆𝑆𝑆𝑆 𝑇𝑇𝑜𝑜 𝑇𝑇𝑆𝑆𝑃𝑃𝑆𝑆𝑇𝑇 = 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑒𝑒𝑡𝑡 𝐸𝐸𝑡𝑡 𝑃𝑃𝑡𝑡𝑖𝑖𝑐𝑐×𝑃𝑃𝑖𝑖𝑁𝑁𝑒𝑒 𝑡𝑡𝑒𝑒𝑟𝑟𝑁𝑁𝑖𝑖𝑡𝑡𝑒𝑒𝑟𝑟 𝑐𝑐𝑒𝑒𝑡𝑡 𝑡𝑡𝑡𝑡𝑖𝑖𝑐𝑐
𝑃𝑃𝑖𝑖𝑁𝑁𝑒𝑒 𝑡𝑡𝑎𝑎𝑡𝑡𝑖𝑖𝑎𝑎𝑡𝑡𝑁𝑁𝑎𝑎𝑒𝑒
(14)
𝑇𝑇𝑆𝑆𝐶𝐶𝑇𝑇𝑆𝑆𝑇𝑇𝑃𝑃 = 𝑁𝑁𝑃𝑃𝑚𝑚𝑁𝑁𝑆𝑆𝑆𝑆 𝑇𝑇𝑜𝑜 𝑇𝑇𝑆𝑆𝑃𝑃𝑆𝑆𝑇𝑇 × 𝑇𝑇𝑆𝑆𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑃𝑃 (15)
𝑇𝑇𝑆𝑆𝑂𝑂&𝑀𝑀𝑃𝑃 = 𝑂𝑂&𝑀𝑀𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑃𝑃 × 𝑁𝑁𝑃𝑃𝑚𝑚𝑁𝑁𝑆𝑆𝑆𝑆 𝑇𝑇𝑜𝑜 𝑇𝑇𝑆𝑆𝑆𝑆𝑆𝑆 × 2 × 𝐷𝐷𝑆𝑆𝑆𝑆𝑇𝑇𝑚𝑚𝑛𝑛𝑆𝑆𝑆𝑆 × 𝑂𝑂𝑃𝑃𝐷𝐷 (16)
Eq(17) shows the calculation for total capital cost throughout project lifetime, while Eq(18) computes the
annual operating cost of the system. Eq(19) shows the calculation for annual cost of biogas production, where
AF is the capital recovery factor.
𝑇𝑇𝑇𝑇𝑇𝑇𝑚𝑚𝑆𝑆 𝐶𝐶𝑚𝑚𝑆𝑆𝑆𝑆𝑚𝑚 = ∑ 𝑃𝑃𝑇𝑇𝑖𝑖𝐶𝐶𝐶𝐶𝑃𝑃𝐶𝐶𝐶𝐶𝑖𝑖 + 𝐶𝐶𝑇𝑇𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑇𝑇𝑆𝑆 𝐶𝐶𝐶𝐶𝑃𝑃𝐶𝐶𝐶𝐶 + 𝑇𝑇𝑆𝑆𝐶𝐶𝑇𝑇𝑆𝑆𝑇𝑇𝑃𝑃 (17)
𝐶𝐶𝑛𝑛𝑛𝑛𝑃𝑃𝑚𝑚𝑆𝑆 𝑂𝑂𝑆𝑆𝑆𝑆𝑚𝑚 = ∑ 𝑃𝑃𝑇𝑇𝑖𝑖𝑂𝑂𝑃𝑃𝐶𝐶𝐶𝐶 𝑖𝑖 + 𝐶𝐶𝑇𝑇𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑇𝑇𝑆𝑆 𝑂𝑂𝑃𝑃𝐶𝐶𝐶𝐶 + 𝑇𝑇𝑆𝑆𝑚𝑚𝑛𝑛𝑆𝑆𝑆𝑆𝑇𝑇𝑆𝑆𝑇𝑇𝑚𝑚𝑇𝑇𝑆𝑆𝑇𝑇𝑛𝑛 𝐶𝐶𝑇𝑇𝑆𝑆𝑇𝑇𝑃𝑃 + 𝑇𝑇𝑆𝑆𝑂𝑂&𝑀𝑀𝑃𝑃 (18)
𝑇𝑇𝑇𝑇𝑇𝑇𝑚𝑚𝑆𝑆𝑆𝑆𝑇𝑇𝑆𝑆𝑇𝑇 = 𝑇𝑇𝑇𝑇𝑇𝑇𝑚𝑚𝑆𝑆𝐶𝐶𝑚𝑚𝑆𝑆𝑆𝑆𝑚𝑚 × 𝐶𝐶𝐹𝐹 + 𝐶𝐶𝑛𝑛𝑛𝑛𝑃𝑃𝑚𝑚𝑆𝑆 𝑂𝑂𝑆𝑆𝑆𝑆𝑚𝑚 (19)
Following total cost calculation is sales price calculation for each utilization options. The option includes
domestic cooking, industrial heating, natural gas vehicle (NGV), natural gas grid and electricity. Bio-CNG is
used for domestic cooking, industrial heating, NGV and natural gas grid. The sales revenue of bio-CNG,
SalesprBioCNG (USD/y) and electricity, SalesprElec (USD/y) is calculated using Eq(20) and Eq(21). The price of
Bio-CNG, Price of BioCNG(USD/MJ) is multiplied with the total biomethane demand, Biodemand (m3/h), heating
value of methane, HVCH4 (MJ/kg) and density of methane to obtain the total price. The sales revenue of
electricity is determined by multiplying the total biomethane demand for electricity, BioElectricity (m3/h), heat rate,
HR (kWh/MJ), heating value of methane, density of methane, the Feed-in-Tariff value, FiT (USD/kWh) and the
annual operating hours. Eq(22) computes the total sales revenue per year.
𝑆𝑆𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝑖𝑖𝐸𝐸𝐸𝐸𝑁𝑁𝐵𝐵 = 𝐻𝐻𝑉𝑉𝐸𝐸𝐶𝐶4 × 𝜌𝜌𝐸𝐸𝐶𝐶4 × 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑇𝑇𝑜𝑜 𝐵𝐵𝑆𝑆𝑇𝑇𝐶𝐶𝑁𝑁𝐵𝐵 × 𝐵𝐵𝑆𝑆𝑇𝑇𝑟𝑟𝑒𝑒𝑁𝑁𝑡𝑡𝑛𝑛𝑟𝑟 × 𝐿𝐿𝑇𝑇 (20)
𝑆𝑆𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐸𝐸𝑎𝑎𝑒𝑒𝑒𝑒 = 𝐻𝐻𝑅𝑅 × 𝐻𝐻𝑉𝑉𝐸𝐸𝐶𝐶4 × 𝜌𝜌𝐸𝐸𝐶𝐶4 × 𝐹𝐹𝑆𝑆𝑇𝑇 × 𝐵𝐵𝑆𝑆𝑇𝑇𝐸𝐸𝑎𝑎𝑒𝑒𝑒𝑒𝑡𝑡𝑡𝑡𝑖𝑖𝑒𝑒𝑖𝑖𝑡𝑡𝑒𝑒 × 𝐿𝐿𝑇𝑇 (21)
𝑆𝑆𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 = 𝑆𝑆𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝑖𝑖𝐸𝐸𝐸𝐸𝑁𝑁𝐵𝐵 + 𝑆𝑆𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐸𝐸𝑎𝑎𝑒𝑒𝑒𝑒 (22)
The calculation for annual profit and simple payback period is shown in Eq(23) and Eq(24). Annual profit is
obtained by the subtraction of annual operating cost from the annual sales. The simple payback period can
then be computed by dividing the total capital cost with the annual profit.
𝐶𝐶𝑛𝑛𝑛𝑛𝑃𝑃𝑚𝑚𝑆𝑆 𝑃𝑃𝑆𝑆𝑇𝑇𝑜𝑜𝑆𝑆𝑇𝑇 = 𝑆𝑆𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐶𝐶𝑛𝑛𝑛𝑛𝑃𝑃𝑚𝑚𝑆𝑆 𝑂𝑂𝑆𝑆𝑆𝑆𝑚𝑚 (23)
𝑆𝑆𝑆𝑆𝑚𝑚𝑆𝑆𝑆𝑆𝑆𝑆 𝑃𝑃𝑚𝑚𝑃𝑃𝑁𝑁𝑚𝑚𝑆𝑆𝑇𝑇 = 𝑃𝑃𝐸𝐸𝑡𝑡𝑡𝑡𝑎𝑎 𝐸𝐸𝑡𝑡𝑐𝑐𝑒𝑒𝐶𝐶
𝐴𝐴𝑛𝑛𝑛𝑛𝑁𝑁𝑡𝑡𝑎𝑎 𝑃𝑃𝑡𝑡𝐸𝐸𝑡𝑡𝑖𝑖𝑡𝑡
(24)
The volumetric balance (equality constraints) for this model is shown through Eq(25) to Eq(27). Eq(25)
indicates that the total amount of biogas available at the start has to be equal to the total volume of biogas
sent to each purification technology. Eq(26) shows that all purified biogas is to be transported via truck or
pipeline to utilization. Eq(27) indicates that the processed biogas is either used to generate electricity or used
as Bio-CNG.
𝐹𝐹𝐵𝐵𝑖𝑖𝐸𝐸𝐵𝐵𝑡𝑡𝐵𝐵 = ∑ 𝐹𝐹𝑖𝑖𝑖𝑖 (25)
∑ 𝐹𝐹𝑖𝑖𝑖𝑖 = 𝐵𝐵𝑆𝑆𝑇𝑇𝑉𝑉𝑃𝑃 + 𝐵𝐵𝑆𝑆𝑇𝑇𝑉𝑉𝑃𝑃 (26)
𝐵𝐵𝑆𝑆𝑇𝑇𝑉𝑉𝑃𝑃 + 𝐵𝐵𝑆𝑆𝑇𝑇𝑉𝑉𝑃𝑃 = 𝐵𝐵𝑆𝑆𝑇𝑇𝐸𝐸𝑎𝑎𝑒𝑒𝑒𝑒𝑡𝑡𝑡𝑡𝑖𝑖𝑒𝑒𝑖𝑖𝑡𝑡𝑒𝑒 + 𝐵𝐵𝑆𝑆𝑇𝑇𝑟𝑟𝑒𝑒𝑁𝑁𝑡𝑡𝑛𝑛𝑟𝑟 (27)
3. Case study and data collection
In order to show the applicability of the model, a hypothetical case study is performed to obtain the optimal
biogas process pathway. In this research, Pasir Gudang district in Johor is taken as a case study. The
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estimated biomethane production from POME based on CPO production of local palm oil mill located in Pasir
Gudang is 2.3 ×106 m3/y (Chin et al., 2013). The COD level in POME is 51 g/L (Zainal et al., 2017). Methane
heating value is 50 MJ/kg and density is 0.656 kg/m3.
The other data for this research is extracted from different sources. Among required data are capital cost
(CAPEX) and operating and maintenance cost (OPEX) of purification technology, transportation mode (truck
and pipeline), and compressor. The distance from identified locations to substations, sales price of Bio-CNG,
sales price of electricity, FiT, electricity tariff and capital recovery factor should also be identified.
For purification technology, the CAPEX for water scrubber is 3,333 USD/m3/h, pressure swing absorption is
5,888 USD/m3/h, membrane separation is 2,824 USD/m3/h, chemical absorption is 3,298 USD/m3/h and
physical absorption is 3,040 USD/m3/h. The operating and maintenance cost of water scrubber is 4.74 × 10-3
USD/kWh, pressure swing absorption is 3.38 × 10-3 USD/kWh, membrane separation is 1.57 × 10-3 USD/kWh,
chemical absorption is 1.82 × 10-3 USD/kWh and physical absorption is 2.46 × 10-3 USD/kWh. For the energy
consumption of the separation unit, the energy requirement for water scrubber is 0.2 kWh/m3, pressure swing
absorption is 0.23 kWh/m3, membrane separation is 0.12 kWh/m3, chemical absorption is 0.15 kWh/m3 and
physical absorption is 0.22 kWh/m3.
As for the compressor, the purchase price of compressor is 276 USD/m3/h. The tariff used to operate the
compressor is taken as 0.09 USD/kWh. The adiabatic efficiency is assumed as 70 %. The biomethane at inlet
has a molecular weight of 19 kg/kmol, specific heat ratio of 1.3, initial temperature of 536.67 deg R and initial
pressure of 14.7 psia. The final pressure required for truck and pipeline transportation are 2900 psia and 290
psia.
For transportation, the truck capacity is 30 m3 per truck. Price of truck is 34,554.35 USD and operating and
maintenance cost is 0.09 USD/km. The truck is assumed to travel at 70 km/h and is working 8 hours a day.
The loading and unloading time is assumed as 2 hours. For pipeline transportation, it is assumed that the gas
pipeline will be constructed by Gas Malaysia and the user are required to pay 0.45 USD/ MMBtu to use the
facility.
Sales price of Bio-CNG is 8.68 USD/GJ and electricity generated from biogas is 0.077 USD/kWh. The power
plant is assumed to have a heat rate of 0.1206 kWh/MJ.
In this case study, different target locations are chosen to supply biogas. There are several targeted locations
identified within Pasir Gudang that could utilize energy from POME biogas. The total distance to all these
locations from the palm oil mill is 33.6 km. The lifetime of the project is assumed as 25 y and capital recovery
factor of 0.071. The plant is assumed to be working 24 hours a day and 365 days a year.
4. Result and discussion
This section discusses the mathematical optimization result, where the optimal biogas supply pathway with the
greatest profit will be determined. Sensitivity result is also conducted to investigate the effect of Bio-CNG price
on the optimal biogas supply pathway.
4.1 Biogas process pathway optimization
The problem is coded in the software General Algebraic Modelling System (GAMS), version 24.7 (GAMS,
2016), where the solver CPLEX is used to solve the associated mixed-integer linear programming problem
(MILP). The results obtained from GAMS shows that the objective to optimize the net profit is 6.51 ×105
USD/y. The cost for membrane separation is 5.69 ×104 USD/y, with a CAPEX of 7.40 ×105 USD and OPEX of
4.41×103 USD/y. The pipeline cost is 3.21×104 USD/y with electricity sales of 7.77 × 105 USD/y. The optimal
pathway of biogas production, transportation and utilization is by using membrane separation as purification
technology, pipeline as the transportation mode to transport biogas to the targeted distribution centre and
utilizing it in the form of electricity. From the optimization result, the payback period for the offsite project is
identified as 1.15 y. Membrane separation is chosen as a profitable purification technology because it has a
number of merits, including low cost, high energy efficiency and involves a simple process (Sun et al., 2015).
This technology allows H2S, CO2 and H2O to pass through the membrane while retaining CH4 on the inlet side.
Pipeline transportation is chosen in this optimization because for truck transportation, the average capacity of
a truck ranges from 30-60 m3. In order to transport biogas in higher scale, more trucks will be required and
considering fuel, operating and maintenance cost of each trip, opting for truck will not be profitable. For
utilization, electricity is chosen in the mathematical optimization because in Malaysia there is already a FiT
scheme for the usage of biogas as electricity while other source does not have financial aids or subsidy in
place. To investigate the suitable rate of subsidy for Bio-CNG, sensitivity analysis is conducted in the following
section by varying the price of Bio-CNG and analyzing the outcome.
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4.2 Bio-CNG subsidy
The result obtained did not recommend the utilization of biogas as Bio-CNG as its selling price is less
profitable than the electricity. This suggests the need for financial aid to make the Bio-CNG utilization more
feasible. In this section, an analysis is conducted to determine the subsidy required for offsite Bio-CNG as
shown in Table 1. Based on Table 1, it can be seen that only when the Bio-CNG sales price increases to 10.4
USD/GJ that the model chooses Bio-CNG utilization as the most optimal option for maximum profit.
Table 1: Analysis on different prices of Bio-CNG
Sales price of Bio-CNG (USD/GJ) FiT (USD/y) Chosen utilization option
8.68 0.077 Electricity
9.8 0.077 Electricity
10.4 0.077 Bio-CNG
5. Conclusions
Malaysia has a high potential to develop biogas industry due to the abundance of POME as a biogas source.
Most of these resources are now under-utilized and the analysis shows that the Malaysian Government needs
to provide more incentive to boost biogas from POME development in the country. The model presented in
this study has seen to be capable to optimize the cost of a POME biogas system that takes into account
purification technologies, transportation modes, and utilization options. Through this study, the net profit of the
biogas project is determined as 6.51 ×105 USD/y with payback period of 1.15 y. The optimal biogas
processing and utilization pathway involves the membrane separation of raw biogas, pipeline transportation to
desired sites, and generation of electricity using biogas. This model is beneficial for energy engineers, and
energy policymakers to plan for future energy developments. In the future, a more detailed study will be
conducted including the specific energy demand that is required by the nearby towns and spatial analysis.
Acknowledgements
The authors would like to acknowledge Universiti Teknologi Malaysia for the research grants with vote number
of 02M03, 00L51, 4C298, and 06G47 that was provided for this research study.
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