Salah Jellali
email: s.jellali@squ.edu.om

Yassine Charabi
email: yassine@squ.edu.om

Muhammad Usman
email: muhammad.usman@squ.edu.om

Abdullah Al-Badi
email: albadi@squ.edu.om

Mejdi Jeguirim
email: mejdi.jeguirim@uha.fr

Investigations on Biogas Recovery from Anaerobic Digestion of Raw Sludge and Its Mixture with Agri-Food Wastes: Application to the Largest Industrial Estate in Oman

Keywords: sludge, agri-food wastes, biogas, electricity, greenhouse gas emission, feasibility study

This work is intended to evaluate the technical, environmental, and economic feasibility of converting the sludge produced at an industrial estate's wastewater treatment plant (WWTP) in Oman into energy through anaerobic digestion (AD). In this study, three different scenarios were analyzed. They concerned the digestion of the total amount of the produced sludge alone (240 m 3 day -1 ) (scenario 1), and its co-digestion with wet agri-food wastes (AFW) at rates of two tonnes day -1 (scenario 2) and ten tonnes day -1 (scenario 3). Based on the analyses of sludge samples, an intensive literature review regarding sludge and AFW Physico-chemical and energetic characteristics and the use of the cost-benefit analysis (CBA) approach, it was found that, for the overall duration of the project (20 years), the AD of the sludge alone (scenario 1) permitted the production of 43.9 GWh of electricity, the reduction of greenhouse gas (GHG) emissions (more than 37,000 tonnes equivalent CO 2 (TCO 2 )) and exhibited positive net present value (NPV: $393,483) and an internal return rate (IRR) of 19.4%. Co-digesting sludge with AFW significantly increased all of these key performance indicators. For instance, scenario 3 results in the recovery of electrical energy of 82.2 GWh and avoids the emission of 70,602 tCO 2 . Moreover, a higher NPV and IRR of $851,876 and 21.8%, respectively, and a payback period (PBP) of only seven years were calculated. The sensitivity analysis revealed that a decrease in total expenses by 15% results in a significant increase of the NPV and the IRR to $1,418,704 and 33.9%, respectively, for scenario 3. Considering a pessimistic assumption (an increase of the total expenses by 15%), all studied scenarios remain attractive. For instance, for scenario 3, the NPV, IRR, and PBP were evaluated to $285,047, 13.5%, and 9 years, respectively. Therefore, the co-digestion of sludge with agri-food wastes for energy recovery purposes could be considered a promising, eco-friendly, and economically viable approach in the Omani industrial estates.

Introduction

Enormous amounts of sludge are produced worldwide in wastewater treatment plants (WWTP) [START_REF] Gherghel | A review on wastewater sludge valorisation and its challenges in the context of circular economy[END_REF]. These solid wastes could represent a real threat to the environment and human health [START_REF] Fijalkowski | The presence of contaminations in sewage sludge-The current situation[END_REF]. Therefore, concerned stakeholders, including public/private organisms, scientists, and civil society, are looking forward to minimize their production [START_REF] Collivignarelli | What Advanced Treatments Can Be Used to Minimize the Production of Sewage Sludge in WWTPs?[END_REF] and to find out the adapted and sustainable management solutions [START_REF] Gherghel | A review on wastewater sludge valorisation and its challenges in the context of circular economy[END_REF]. These solutions should be technically feasible, economically viable, eco-friendly, and socially acceptable [START_REF]Economic and Social Impacts of the Use of Sewage Sludge on Land[END_REF]. Various approaches and technologies have been applied to reduce their negative impacts on the environment and/or to convert them into valuable resources. Such technologies mainly include dumping in wild/controlled landfills and composting for subsequent use in agriculture, fabrication of building materials, and energy extraction [START_REF] Seleiman | Recycling sludge on cropland as fertilizer-Advantages and risks[END_REF][START_REF] Chang | Valorization of sewage sludge in the fabrication of construction and building materials: A review[END_REF][START_REF] Raheem | Opportunities and challenges in sustainable treatment and resource reuse of sewage sludge: A review[END_REF]. Sludge valorization for energy recovery has emerged as a promising and sustainable approach since it permits converting them into energy (electricity or heat or electricity/heat) that could be used directly in situ for the WWTP's functioning. The principal used technologies for this purpose include combustion, gasification, pyrolysis, and anaerobic digestion (AD) [START_REF] Kor-Bicakci | Recent developments on thermal municipal sludge pretreatment technologies for enhanced anaerobic digestion[END_REF][START_REF] Cao | Sewage sludge-to-energy approaches based on anaerobic digestion and pyrolysis: Brief overview and energy efficiency assessment[END_REF][START_REF] Oladejo | A Review of Sludge-to-Energy Recovery Methods[END_REF]. The AD process is a biological process by which the organic compounds contained in a given solid/liquid waste are converted into biogas by using microorganisms. This process involves a series of four biochemical stages including [START_REF] Oladejo | A Review of Sludge-to-Energy Recovery Methods[END_REF][START_REF] Lee | Effects of solids retention time on methanogenesis in anaerobic digestion of thickened mixed sludge[END_REF]: (i) hydrolysis, where complex organic molecules are converted into simple sugars, fatty acids, and peptides; (ii) acidogenesis consisting in the fermentation of the hydrolysis products into short-chain volatile organic acids such as alcohols, butyrate, carbonic acids, and propionates; (iii) acetogenesis where the latter products are converted into acetate, carbon dioxide, and hydrogen; and (iv) methanogenesis where these by-products were converted into methane. Compared to the other technologies, the AD process is highly advantageous due to its lower cost, lower energy consumption, and its ability to produce biogas, which is composed mainly of 60-70% of methane, 30-40% of carbon dioxide, and traces of other gases such as H 2 S [START_REF] Cao | Sewage sludge-to-energy approaches based on anaerobic digestion and pyrolysis: Brief overview and energy efficiency assessment[END_REF][START_REF] Oladejo | A Review of Sludge-to-Energy Recovery Methods[END_REF]. This biogas can be either cleaned and upgraded to produce bio-methane (that can substitute the natural gas) using water scrubbers [START_REF] Aryal | Alternative of Biogas Injection into the Danish Gas Grid System-A Study from Demand Perspective[END_REF] or converted into heat or electricity via thermal reactors such as boilers, turbines, and generators [START_REF] Cao | Sewage sludge-to-energy approaches based on anaerobic digestion and pyrolysis: Brief overview and energy efficiency assessment[END_REF][START_REF] Oladejo | A Review of Sludge-to-Energy Recovery Methods[END_REF]. The generated energy could be used in the WWTP covering a significant proportion of its needs or even sold to the supply grid [START_REF] Mills | Environmental & economic life cycle assessment of current & future sewage sludge to energy technologies[END_REF][START_REF] Shen | An overview of biogas production and utilization at full-scale wastewater treatment plants (WWTPs) in the United States: Challenges and opportunities towards energy-neutral WWTPs[END_REF]. Therefore, through the biogas recovery, the AD installations could represent a concrete opportunity for WWTPs to improve their energy independence. WWTPs can further reduce their operational costs and increase their overall environmental performance by shifting from fossil fuels to renewable energy production and reuse [START_REF] Shen | An overview of biogas production and utilization at full-scale wastewater treatment plants (WWTPs) in the United States: Challenges and opportunities towards energy-neutral WWTPs[END_REF].

Anaerobic digestion is being applied as a sustainable way to manage the produced sludge in WWTPs in various countries in the world [START_REF] Shen | An overview of biogas production and utilization at full-scale wastewater treatment plants (WWTPs) in the United States: Challenges and opportunities towards energy-neutral WWTPs[END_REF][START_REF] Wei | Development, current state and future trends of sludge management in China: Based on exploratory data and CO2-equivaient emissions analysis[END_REF]. For instance, in 2019, in China, about 6.8% of the total produced sludge (2.68 million tonnes (wet basis)) were treated by this technology [START_REF] Wei | Development, current state and future trends of sludge management in China: Based on exploratory data and CO2-equivaient emissions analysis[END_REF]. They are theoretically generating 132 Mm 3 of methane and 1.47 million tons of fertilizer [START_REF] Wei | Development, current state and future trends of sludge management in China: Based on exploratory data and CO2-equivaient emissions analysis[END_REF]. In the Unites States of America (USA), in 2017, about 1240 large-scale WWTPs were equipped with anaerobic digesters [START_REF] Scarlat | Biogas: Developments and perspectives in Europe[END_REF]. In the European Union (EU), at the end of the last decade, approximately 50% of the WWTPs were equipped with anaerobic digestion facilities [START_REF] Werle | A review of methods for the thermal utilization of sewage sludge: The Polish perspective[END_REF]. According to the latest report published in 2020 by the EurObserv'ER barometer which measures the progress made by renewable energies in each of the 28 countries of the EU [18], the overall primary energy production from biogas was estimated to be 16,629.8 Kilotonne of Oil Equivalent (KTOE). The contribution of the sewage sludge was determined to be more than 1593 KTOE (about 9.6%). In addition, the gross amount of produced electricity from biogas generated from the AD of biomasses including sludge was estimated to about 62,463 GWh. This electricity was mostly produced by Germany, Italy, and United Kingdom with percentages of 52.6%, 13.3%, and 12.1%, respectively.

In addition to the sludge from WWTPs, in industrial estates, large amounts of agrifood wastes (AFW) are produced [START_REF] Torres-León | Food Waste and Byproducts: An Opportunity to Minimize Malnutrition and Hunger in Developing Countries[END_REF]. These wastes are not appropriately exploited since they are generally dumped in landfills, where they could constitute a serious threat to the environment and human health [START_REF] Torres-León | Food Waste and Byproducts: An Opportunity to Minimize Malnutrition and Hunger in Developing Countries[END_REF]. Simultaneously, various AFW has higher energetic potential production than sludge due to their more important volatile organic matter contents and degradation rates [START_REF] Czekała | Agricultural Biogas Plants as a Chance for the Development of the Agri-Food Sector[END_REF][START_REF] Król | Testing properties of sewage sludge for energy use[END_REF][START_REF] Ahmad | Characterization of energy content in food waste by using thermogravimetric analyser (TGA) and elemental analyser (CHNS-O)[END_REF]. Indeed, these two parameters' average values are assessed to 90% and 75% for AFW [START_REF] Zhang | Reviewing the anaerobic digestion of food waste for biogas production[END_REF][START_REF] Kuo | Biogas production from anaerobic digestion of food waste and relevant air quality implications[END_REF] and only 45% and 48% for sludge [START_REF] Oladejo | A Review of Sludge-to-Energy Recovery Methods[END_REF][START_REF] Bertanza | Towards energy self-sufficiency and integral material recovery in waste water treatment plants: Assessment of upgrading options[END_REF], respectively. Therefore, the co-digestion of sludge with AFW has emerged as an interesting way to manage these two kinds of solid wastes [START_REF] Keucken | Anaerobic Co-Digestion of Sludge and Organic Food Waste-Performance, Inhibition, and Impact on the Microbial Community[END_REF][START_REF] Guimarães | Construction of Biodigesters to Optimize the Production of Biogas from Anaerobic Co-Digestion of Food Waste and Sewage[END_REF][START_REF] Morales-Polo | Reviewing the Anaerobic Digestion of Food Waste: From Waste Generation and Anaerobic Process to Its Perspectives[END_REF].

Oman has established nine industrial estates in various regions of the country. Al-Russayl, in Muscat, is the largest industrial estate in the country. This industrial estate collects and treats all the produced wastewaters in a centralized WWTP. Due to the significant volumes of the generated sludge, its handling in this WWTP represents a substantial environmental and social concern. Furthermore, despite their significant energy potential and other valuable resource contents, the whole amount of the produced sludge is dumped into a landfill after its dewatering and drying. This operation might have an important environmental negative impact on water and soil resources and air through the emission of GHG. Thus, this sludge's treatment/valorization (through AD process) could partially resolve these social and environmental issues and offer a relevant economic opportunity to convert it into energy (especially electricity). This generated energy could be injected into the national distribution company grid or directly used in the WWTP to substitute the commercial electricity.

On the other hand, despite the proven efficiency of the AD process for WWTPs' sludge and AFW at both laboratory and field scales, relatively few studies have focused on the technical, environmental, and economic viability of this technology at industrialmoderate-sized WWTPs by using tailored approaches such as the cost-benefit analysis method (CBA). Indeed, CBA has been pointed out among various available economic analytical tools as a well-established method for assessing the projects' viability dealing with solid wastes conversion into energy through AD process [START_REF] Mohammed | Feasibility study for biogas integration into waste treatment plants in Ghana. Egypt[END_REF]. This method allows the determination, versus time, of various cost and benefits indicators essential for facilitating decision-makers' help and orientation. Therefore, this work's main objective is to study the technical, environmental, and economic feasibility of converting the sludge produced at Al-Russayl industrial estate into electricity through the AD process. The economic efficiency of its co-digestion with agri-food wastes produced at the same industrial estate will also be assessed under various options.

Materials and Methods

WWTP of the Al Russayl Industrial Estate

This study concerns the Al Russayl industrial estate which is the largest one in Oman. It covers 10.8 km 2 and contains 334 industries operating in various sectors, including mainly agri-food, steel, aluminum, textile, etc.

According to a 2019 estimation, the average consumed water in this industrial estate is about 4639 m 3 day -1 . The entire wastewater amount generated by this industrial estate is collected and treated by a centralized WWTP. In 2019, the average treated wastewater amount in this WWTP was assessed to be about 2270 m 3 day -1 . The design, main operating parameters, and the flow diagram for wastewater and sludge in this WWTP are given in Figure 1. The wastewater treatment plant is constituted of the following systems: (i) a bar screen chamber that removes objects having size higher than 3 cm such as plastics, stones, and wood wastes etc.; (ii) a balancing tank with a volume of 420 m 3 where the wastewater is collected and homogenized; (iii) a dissolved air flotation unit where the air injection at a flow rate of 200 m 3 h -1 is applied to remove oil and greases; (iv) coagulation-flocculation tanks that permit the removal of suspended and colloidal solids; (v) an anoxic tank, having a volume of 362 m 3 , that allows the denitrification of wastewater; (vi) a moving bed bioreactor (MBBR) tank with a volume capacity of 796 m 3 allowing the removal of the organic pollutants, vii) a clarifier with a volume of 1250 m 3 where the wastewaters are separated from the sludge that was created during the biological treatment; viii) a chlorine tank with a volume of 165 m 3 that permits the disinfection of the treated wastewaters; and (ix) three parallel tertiary filtration units filled with various materials (from up to bottom: anthracite, activated carbon, fine sand, silex, fine pebbles, and finally coarse pebbles). The discharged wastewater after treatment has a physicochemical-biological quality that permits its reuse for the irrigation of surrounding green spaces. The total produced sludge amount by this WWTP is 240 m 3 day -1 (Figure 1). It is collected from both the coagulation-flocculation and the MBBR biological treatment units at equivalent amounts (120 m 3 day -1 for each one). The produced sludge's water content varies between 95% and 98%, with an average value of 96.5%. This sludge is dewatered in situ by adding various chemicals (like polymers) and centrifugation. The dewatered sludge with a water content of about 75% is then sun-dried inside the WWTP site and then transferred to landfills for dumping. Therefore, this sludge's adapted management represents an important task to be urgently undertaken to turn them into valuable resources (energy recovery, for instance).

Preliminary Characterization of Sludge

The sludge of Al Russayl industrial estate was subjected to a preliminary characterization including (i) pH determination for a solid-liquid ratio of 1:5 by a precisely calibrated electrode, (ii) total organic carbon assessment by using the Walkley-Black method, and (iii) the majority of the heavy metals contents were determined through an inductively coupled plasma, mass spectroscopy (ICP-MS) apparatus after a solid-liquid extraction according to the experimental protocol given by Khadhar et al. [START_REF] Khadhar | Integration of sequential extraction, chemical analysis and statistical tools for the availability risk assessment of heavy metals in sludge amended soils[END_REF]. A selective electrode quantified fluoride contents.

Methods and Data Used for the Feasibility Study

The technical, environmental, and economic feasibility of the conversion of the produced sludge in the WWTP of Al-Russayl into energy by the AD process was carried out for the following three scenarios: Scenario 1: The anaerobic digestion of the sludge alone produced in the WWTP; Scenario 2: The anaerobic co-digestion of the sludge produced in the WWTP mixed with 2 tonnes day -1 of agri-food wastes (wet basis); The total produced sludge amount by this WWTP is 240 m 3 day -1 (Figure 1). It is collected from both the coagulation-flocculation and the MBBR biological treatment units at equivalent amounts (120 m 3 day -1 for each one). The produced sludge's water content varies between 95% and 98%, with an average value of 96.5%. This sludge is dewatered in situ by adding various chemicals (like polymers) and centrifugation. The dewatered sludge with a water content of about 75% is then sun-dried inside the WWTP site and then transferred to landfills for dumping. Therefore, this sludge's adapted management represents an important task to be urgently undertaken to turn them into valuable resources (energy recovery, for instance).

Preliminary Characterization of Sludge

The sludge of Al Russayl industrial estate was subjected to a preliminary characterization including (i) pH determination for a solid-liquid ratio of 1:5 by a precisely calibrated electrode, (ii) total organic carbon assessment by using the Walkley-Black method, and (iii) the majority of the heavy metals contents were determined through an inductively coupled plasma, mass spectroscopy (ICP-MS) apparatus after a solid-liquid extraction according to the experimental protocol given by Khadhar et al. [START_REF] Khadhar | Integration of sequential extraction, chemical analysis and statistical tools for the availability risk assessment of heavy metals in sludge amended soils[END_REF]. A selective electrode quantified fluoride contents.

Methods and Data Used for the Feasibility Study

The technical, environmental, and economic feasibility of the conversion of the produced sludge in the WWTP of Al-Russayl into energy by the AD process was carried out for the following three scenarios: Scenario 1: The anaerobic digestion of the sludge alone produced in the WWTP; Scenario 2: The anaerobic co-digestion of the sludge produced in the WWTP mixed with 2 tonnes day -1 of agri-food wastes (wet basis); Scenario 3: The anaerobic co-digestion of the sludge produced in the WWTP mixed with 10 tonnes day -1 of agri-food wastes (wet basis); Table 1 summarizes the technical, environmental, and economic assumptions and indicators to assess the biogas production and its conversion into electricity in the studied WWTP. All the used parameter values were taken from the literature. Whenever possible, average values given by various studies are calculated and used (Table 1). All the prices given in this manuscript are provided in United States dollars ($). ) 1020 [START_REF] Oladejo | A Review of Sludge-to-Energy Recovery Methods[END_REF] Solid matter content in the thickened sludge (%) 25 [START_REF] Cao | Sewage sludge-to-energy approaches based on anaerobic digestion and pyrolysis: Brief overview and energy efficiency assessment[END_REF] Volatile matter (VM) content in sludge (%) 45.0 [START_REF] Oladejo | A Review of Sludge-to-Energy Recovery Methods[END_REF] Volatile matter conversion rate of sludge (%) 45.0 [START_REF] Bertanza | Towards energy self-sufficiency and integral material recovery in waste water treatment plants: Assessment of upgrading options[END_REF] C/N ratio range 6-10 [START_REF] Chow | Anaerobic Co-Digestion of Wastewater Sludge: A Review of Potential Co-Substrates and Operating Factors for Improved Methane Yield[END_REF] Biogas production per kg of degraded VM of sludge (m 3 kg -1 ) 1.0 [START_REF] Cao | Sewage sludge-to-energy approaches based on anaerobic digestion and pyrolysis: Brief overview and energy efficiency assessment[END_REF][START_REF] Kuo | Biogas production from anaerobic digestion of food waste and relevant air quality implications[END_REF] Initial AFW flow rate (2021) (tonnes day -1 ), wet basis-Scenario 2 2.0 This study, baseline option Solid matter content in agri-food wastes (%) 20.0 [START_REF] Islam | Methane Production Potential of Food Waste and Food Waste Mixture with Swine Manure in Anaerobic Digestion[END_REF][START_REF] Zhang | Batch and semi-continuous anaerobic digestion of food waste in a dual solid-liquid system[END_REF] Initial AFW flow rate (2021) (tonnes day Volatile matter content in agri food waste (%) 90.0 [START_REF] Zhang | Batch and semi-continuous anaerobic digestion of food waste in a dual solid-liquid system[END_REF] Volatile matter of AFW conversion rate (%) 75.0 [START_REF] Kuo | Biogas production from anaerobic digestion of food waste and relevant air quality implications[END_REF] C/N ratio range 11-21 [START_REF] Chow | Anaerobic Co-Digestion of Wastewater Sludge: A Review of Potential Co-Substrates and Operating Factors for Improved Methane Yield[END_REF] Biogas production per kg of degraded VM of food wastes (m 3 kg -1 ) 1.1 [START_REF] Kuo | Biogas production from anaerobic digestion of food waste and relevant air quality implications[END_REF] Electricity generation

Methane content in biogas (%) 65.0 [START_REF] Kuo | Biogas production from anaerobic digestion of food waste and relevant air quality implications[END_REF] Lower methane energy content (MJ m -3 ) 35.8 [START_REF] Król | Testing properties of sewage sludge for energy use[END_REF] Thermal conversion factor (%) 45.0 [START_REF] Akbulut | Techno-economic analysis of electricity and heat generation from farm-scale biogas plant: Çiçekda gı case study[END_REF]

Gas emission reduction

Electricity Grid emission factor (tCO 2 MWh -1 ) 0.858 [START_REF] Charabi | Strategic pathways and regulatory choices for effective GHG reduction in hydrocarbon based economy: Case of Oman[END_REF] Table 1. Cont.

Biogas Generation Reference Parameter Value

Sludge transport factor (tCO 2 per 1000 km) 0.113 This study, baseline option Emission reduction benefits rate ($per tCO 2 ) 2.587 [START_REF] Hamrick | State of the Voluntary Carbon Markets[END_REF] Electricity selling

Omani electricity price for businesses ($kWh -1 ) 0.148 Internal report

Produced electricity from biogas selling price ($kWh -1 ) 0.138 In this study, the baseline option

The project costs include (i) the digester acquisition, (ii) the biogas conversion into electricity (CO 2 separation step, and electricity generators), and (iii) the operational and maintenance costs:

•

The digester price (D p ) was evaluated according to the empirical formula given by Bidart et al. [START_REF] Bidart | Electricity and substitute natural gas generation from the conversion of wastewater treatment plant sludge[END_REF]:

D p = 18248 * Q b 0.8586 (1)
where Q b is the produced biogas amount per hour (m 3 h -1 ).

•

The average annual cost (investment, operating, and maintenance) of the biogas conversion into electricity through generators was fixed to $0.07 kWh -1 produced. Almost similar values were proposed by Bidart et al. [START_REF] Bidart | Electricity and substitute natural gas generation from the conversion of wastewater treatment plant sludge[END_REF] and Morin et al. [START_REF] Morin | Economic and environmental assessment on the energetic valorization of organic material for a municipality in Quebec, Canada[END_REF].

•

The annual costs related to the digester's operating and maintenance were fixed to 3% of the capital investment. It is in agreement with the one proposed by Martin [START_REF] Martin | A Protocol for Quantifying and Reporting the Performance of Anaerobic Digestion Systems for Livestock Manures[END_REF] and exists in the proposed range by the United States Department of Agriculture (USDA, 2007). This value is higher than the proposed rate suggested by Mohammed et al. [START_REF] Mohammed | Feasibility study for biogas integration into waste treatment plants in Ghana. Egypt[END_REF] when carrying out a feasibility study of biogas integration into Ghana's waste treatment plants (1%).

The projected incomes of the baseline option are composed of:

•

The electricity production revenue (EPR) is equal to the produced amount multiplied by its selling price. This price was fixed to $0.138 kWh -1 , which is $0.01 lower than the current price by the Omani electricity distribution company ($0.148 kWh -1 ).

•

The Certified Emissions Reduction (CER) benefits due to electricity generation from biogas. It is equal to the produced electricity from biogas multiplied by the electricity grid emission factor (EGEF). This factor depends mainly on the used feedstock and technology for electricity production. The EGEF has decreased significantly during the last two decades due to the adoption of cleaner technologies. In 2016, its average value in Europe was estimated to 0.296 tCO 2 MWh -1 . It is only 0.113 tCO 2 MWh -1 for Finland, 0.440 tCO 2 MWh -1 for Germany, but reaches 0.812 tCO 2 MWh -1 for Estonia [START_REF]EEA Greenhouse Gas-Data Viewer. Data Viewer Greenhouse Gas Emissions and Removals, Sent by Countries to UNFCCC EU Greenhouse Gas Monitoring Mechanism (EU Member States)[END_REF]. For Oman's case, an average value of 0.858 tCO 2 MWh -1 was proposed by Charabi et al. [START_REF] Charabi | Strategic pathways and regulatory choices for effective GHG reduction in hydrocarbon based economy: Case of Oman[END_REF], corresponding to the use of 97% of natural gas and 3% of diesel for the production of electricity.

The CER benefits due to the decrease of the sludge amount transfer to landfills. The sludge transport factor was calculated to 0.113 tCO 2 per 1000 Km.

Cost-Benefit Analysis

The cost-benefit analysis (CBA) is a financial method that permits to judge the utility and the profitability of a given project. This judgment is based on the assessment of various parameters such as the net present value (NPV), the internal rate of return (IRR), and the payback period (PBP).

The NPV is defined as follows [START_REF] Mohammed | Feasibility study for biogas integration into waste treatment plants in Ghana. Egypt[END_REF]:

NPV = n ∑ t=1 (B t -C t ) (1 + r) t (2)
where B t and C t are the benefits and costs at the year "t", "r" is the discount or interest rate, and "t" is the year number varying between 1 and 20.

The IRR refers to the discount rate, making the NVP of the cash flow equal to zero. It is also considered as the average earning power of the project's expenses over the project life [START_REF] Mohammed | Feasibility study for biogas integration into waste treatment plants in Ghana. Egypt[END_REF]. Finally, the Payback period (PBP) is defined as the number of years necessary to recover the investment. Thus, it corresponds to the period where the cumulated benefits cover the cumulated expenses.

Sensitivity Analysis

The sensitivity of the cost-effectiveness of this project was assessed in comparison with the baseline conditions for the following options:

-Option 1: baseline conditions + generated electricity sold at the current price applied by the Omani distribution company: $0.148 (7.25% higher than the one used for the baseline conditions) -Option 2: Baseline conditions + annual expenses decrease by 15% -Option 3: Baseline conditions + annual expenses increase by 15%

Results and Discussions

Preliminary Physico-Chemical Characterization of Sludge

The sludge physico-chemical characterization shows that it is a slightly acidic media with a pH of 6.6. Its total organic carbon (TOC) was assessed to 21.0%. As expected, TOC content of this industrial sludge is lower than those observed for those collected from urban WWTPs [START_REF] Adani | Long-term effect of sewage sludge application on soil humic acids[END_REF][START_REF] Zhang | Effects of vermicomposting on the main chemical properties and bioavailability of Cd/Zn in pure sludge[END_REF][START_REF] Janowska | Assessment of mobility and bioavailability of mercury compounds in sewage sludge and composts[END_REF]. However, it remains relatively high, permitting the organic matter supply to the micro-organisms to ensure their growth and the biodegradation of the sludge's volatile organic fraction. On the other hand, analyses of the heavy metals showed that except molybdenum, all-metal contents in the sludge were lower than those fixed by the Omani reuse norm in agriculture (Table 2). Molybdenum is most probably discharged in the wastewaters generated by the alloy steel industries operating in this industrial estate. Even if various countries have not yet included molybdenum in the compounds list of their norms [START_REF] Collivignarelli | Legislation for the Reuse of Biosolids on Agricultural Land in Europe: Overview[END_REF], it is recommended to remove this component at the producing sources in Al-Russayl industrial estate utilizing mastered technologies as adsorption onto zeolites or activated carbon [START_REF] Verbinnen | Removal of Molybdate Anions from Water by Adsorption on Zeolite-Supported Magnetite[END_REF][START_REF] Zhu | Removal of Molybdenum(VI) from Raw Water Using Nano Zero-Valent Iron Supported on Activated Carbon[END_REF]. Apart from this component, the calculated ratios between the permissible concentrations fixed by the Omani standards and the measured ones vary between 3.6 and 100. These relatively high ratios suggest that even after the AD process's mass sludge reduction, most of heavy metals contents should remain lower than those fixed by the local reuse norm. It is worth mentioning that the measured sludge heavy metals contents are also lower than the fixed values by the European directive 86/278/EEC [START_REF]Council Directive 86/278/EEC of 12 June 1986 on the protection of the environment, and in particular of the soil, when sewage sludge is used in agriculture[END_REF].

On the other hand, it is essential to underline that a previous analysis of Al-Russayl WWTP's sludge quality [START_REF] Baawain | Characterization of Industrial Wastewater Sludge in Oman from Three Different Regions and Recommendations for Alternate Reuse Applications[END_REF] have shown that the molybdenum content was about two times lower than the norm (11 mg kg -1 ). Moreover, this former study showed that only Cd had contents higher than the Omani fixed norm and the European directive (64.5 mg kg -1 ). Therefore, it is recommended to carry out further sludge samples analyses to understand heavy metals contents better progress with time. This is an essential aspect to consider if valorization of the digested sludge is planned. It is important to underline that high contents of heavy metals in feedstocks could negatively impact the development of methanogens bacteria during the AD process [START_REF] Alrawashdeh | Effect of Heavy Metals in the Performance of Anaerobic Digestion of Olive Mill Waste[END_REF][START_REF] Abdel-Shafy | Biogas production as affected by heavy metals in the anaerobic digestion of sludge. Egypt[END_REF]. Therefore, the co-digestion of this industrial sludge with AFW would potentially contribute to the dilution of heavy metals contents and consequently to improve the blended biomass (sludge and AFW) conversion into biogas.

Biogas and Electricity Production Capacities

The produced sludge and agri-food wastes in generating biogas, methane, and electricity were calculated based on the assumptions presented in Table 1 for the three selected scenarios (see Section 2.5). Owing to the dry and hot climate of Oman, these wastes are expected to be anaerobically digested under mesophilic conditions (temperature between 30 and 38 • C) and for an average residence time of 20 days [START_REF] Cao | Sewage sludge-to-energy approaches based on anaerobic digestion and pyrolysis: Brief overview and energy efficiency assessment[END_REF]. Indeed, low residence times (<10 days) do not allow optimal bacterial growth [START_REF] Lee | Effects of solids retention time on methanogenesis in anaerobic digestion of thickened mixed sludge[END_REF]. Whilst, increasing residence times over 20 days will not permit a significant improvement in volatile matter degradation and biogas production [START_REF] Oladejo | A Review of Sludge-to-Energy Recovery Methods[END_REF][START_REF] Appels | Principles and potential of the anaerobic digestion of waste-activated sludge[END_REF]. Moreover, the use of higher residence time is generally accompanied by higher capital cost (larger size of digester), and requires more energy for process operation such as sludge mixing [START_REF] Cao | Sewage sludge-to-energy approaches based on anaerobic digestion and pyrolysis: Brief overview and energy efficiency assessment[END_REF]. Obtained results (Table 3) showed that the AD of the Al Russayl WWTP sludge alone (scenario 1) has a significant potential for biogas recovery. Indeed, the average annual amounts of biogas and methane were estimated to be more than 0.75 and 0.49 Million m 3 year -1 (Mm 3 year -1 ), respectively. As indicated above, the produced methane amount depends on the quantity and characteristics of the used sludge and the temperature and hydraulic residence time [START_REF] Oladejo | A Review of Sludge-to-Energy Recovery Methods[END_REF][START_REF] Shen | An overview of biogas production and utilization at full-scale wastewater treatment plants (WWTPs) in the United States: Challenges and opportunities towards energy-neutral WWTPs[END_REF]. For that reason, large amounts of methane are produced in bigger WWTPs. For instance, in the Ankara WWTP, the biggest one in Turkey, designed for a daily flow rate of 0.971 Mm 3 day -1 produced through eight anaerobic digesters, a total methane amount than 11.8 Mm 3 year -1 [START_REF] Berktay | Biogas Production and Utilization Potential of Wastewater Treatment Sludge. Energy Sources Part A Recover[END_REF]. During the entire project's lifetime, the biogas and methane amounts from the AD of the sludge alone were assessed to about 15.1 and 9.8 Mm 3 , respectively (Table 3 and Figure 2). This biogas permits producing a total electricity amount of about 43.9 GWh during the 20 years' project duration. The average annual produced electricity corresponds to about 2.2 GWh. This production is about 34.4% higher than the total consumed electricity amount by the WWTP in 2020. It is about 13.5% higher than the average consumed amount in the two previous years that were not affected by the Corona virus pandemic. This calculated generated electricity by Al-Russayl sludge is higher than the one produced in the Rovereto WWTP, Italy (1.4 GWh year -1 ), which treats a lower sludge flow rate (90 m 3 day -1 ). It is lower than those produced in big plants such as those of Ankara, Turkey; Budapest, Hungary, and Philadelphia, the USA, which are producing 25.5, 38.8, and 49.1 GWh year -1 and satisfying about 90% [START_REF] Berktay | Biogas Production and Utilization Potential of Wastewater Treatment Sludge. Energy Sources Part A Recover[END_REF], 65% [START_REF] Gurieff | Moving towards an energy neutral WWTP-The positive impact of ExelysTM continuous thermal hydrolysis in achieving this goal[END_REF], and 54% [START_REF] Tarallo | Demonstrated Energy Neutrality Leadership: A Study of Five Champions of Change[END_REF] of these plants electricity needs, respectively. It is essential to underline that Oman has to carry out massive efforts related to sludge conversion into electricity in Al-Russayl industrial estate and other urban WWTPs producing substantial amounts. This will permit Oman to go in the same direction as some European developed countries who are producing large energy amounts from the AD of sludge only, such as Germany, UK, the Netherlands, and Sweden [START_REF] Bachmann | Sustainable Biogas Production in Municipal Wastewater Treatment Plants[END_REF].

Owing to their higher organic matter contents and anaerobic biodegradability (see Table 1), co-digesting sludge with agri-food wastes has significantly increased the produced biogas, methane, and electricity amounts (Table 3). An increase in agri-food wastes flow rate improves biogas, methane, and electricity production (Figure 2). For instance, when the sludge was mixed with 2 and 10 tonnes day -1 of agri-food wastes, the produced electricity increased from 43.9 GWh by about 17.5% and 87.3% to reach 51.6 and 82.2 GWh, respectively. This is mainly because the agri-food wastes' volatile matter contents, C/N ratio, and degradability capacities are much higher than those of the Al-Russayl WWTP's sludge. Indeed, the AFW' volatile matter contents and C/N of agri-food wastes are about two times higher than that of the sludge [START_REF] Chow | Anaerobic Co-Digestion of Wastewater Sludge: A Review of Potential Co-Substrates and Operating Factors for Improved Methane Yield[END_REF].

Figure 2.

Biogas, methane, and electricity generation capacities during the lifetime project by the digestion of sewage sludge alone (SS) and its co-digestion with agri-food wastes (AFW) (Scenario 1: SS alone; Scenario 2: SS+ 2 tonnes day -1 of AFW; Scenario 3: SS+ 10 tonnes day -1 of AFW). Table 3. Annual and project lifetime (20 years) biogas, methane, and electricity produced amounts from the digestion of Al Russayl WWTP sludge or its co-digestion with agri-food wastes (Scenario 1: SS alone; Scenario 2: SS+ 2 tonnes day -1 of AFW; Scenario 3: SS+ 10 tonnes day -1 of AFW). It is essential to underline that Oman has to carry out massive efforts related to sludge conversion into electricity in Al-Russayl industrial estate and other urban WWTPs producing substantial amounts. This will permit Oman to go in the same direction as some European developed countries who are producing large energy amounts from the AD of sludge only, such as Germany, UK, the Netherlands, and Sweden [START_REF] Bachmann | Sustainable Biogas Production in Municipal Wastewater Treatment Plants[END_REF].

Scenario 1 Scenario 2 Scenario 3 Average annual produced biogas (Mm

Owing to their higher organic matter contents and anaerobic biodegradability (see Table 1), co-digesting sludge with agri-food wastes has significantly increased the produced biogas, methane, and electricity amounts (Table 3). An increase in agri-food wastes flow rate improves biogas, methane, and electricity production (Figure 2). For instance, when the sludge was mixed with 2 and 10 tonnes day -1 of agri-food wastes, the produced electricity increased from 43.9 GWh by about 17.5% and 87.3% to reach 51.6 and 82.2 GWh, respectively. This is mainly because the agri-food wastes' volatile matter contents, C/N ratio, and degradability capacities are much higher than those of the Al-Russayl WWTP's Similar trends were reported by both laboratory and field studies. For instance, at a laboratory scale, Keucken et al. [START_REF] Keucken | Anaerobic Co-Digestion of Sludge and Organic Food Waste-Performance, Inhibition, and Impact on the Microbial Community[END_REF] reported an increase of methane production by 20-40% when co-digesting sludge with organic food wastes at a ratio of 1:1 (based on the volatile matter contents). In addition, Mattioli et al. [START_REF] Mattioli | Co-digestion of the organic fraction of municipal solid waste and sludge improves the energy balance of wastewater treatment plants: Rovereto case study[END_REF] studied the co-digestion of the sludge produced in Rovereto WWTP (Italy) at a flow rate of 90 m 3 day -1 and a solid content percentage of 4.3%, with 10 tonnes day -1 of municipal organic wastes. They reported an increase of the annual biogas production from about 0.482 to 0.993 Mm 3 , doubling the amount of generated power from about 1.4 to 2.8 GWh year -1 . This enabled the plant to recover about 85% of its total energy demand. Furthermore, Koch et al. [START_REF] Koch | Co-digestion of food waste in a municipal wastewater treatment plant: Comparison of batch tests and full-scale experiences[END_REF] studied the digestion of sludge generated from the WWTP of Garching/Alz, Germany, and its co-digestion with 10% of food wastes within a 1350 m 3 digester volume. They showed that the annual methane produced amount increased from 85,494 m 3 year -1 to more than 163,000 m 3 year -1 . This has increased the self-generated energy from 25% to 78%. They imputed this better energy performance during the co-digestion process to the higher C/N ratio of the used food waste (17.7) than the raw sludge (8.8). Finally, Maktabifard et al. [START_REF] Maktabifard | Achieving energy neutrality in wastewater treatment plants through energy savings and enhancing renewable energy production[END_REF], based on a comparative study on 176 WWTPs in Germany, reported that about 44% of these plants could achieve energy neutrality through sludge co-digestion with other organic substrates.

It is worth mentioning that the co-digestion of sludge with an important fraction of AFW could, under certain conditions, negatively impact the AD process due to the excessive presence of Na + and free-ammonia-nitrogen [START_REF] Chow | Anaerobic Co-Digestion of Wastewater Sludge: A Review of Potential Co-Substrates and Operating Factors for Improved Methane Yield[END_REF]. These two components could interfere with the metabolic process of the microbial activity and lead to the accumulation of volatile fatty acids, respectively [START_REF] Chow | Anaerobic Co-Digestion of Wastewater Sludge: A Review of Potential Co-Substrates and Operating Factors for Improved Methane Yield[END_REF]. Koch et al. [START_REF] Koch | Co-digestion of food waste in municipal wastewater treatment plants: Effect of different mixtures on methane yield and hydrolysis rate constant[END_REF] studied the co-digestion of raw sludge and food waste using different mass-based mixtures in batch trials. They showed that sludge co-digestion with food wastes fractions, up to 12.5% (mass-based) or 35% (volatile solids based), significantly improved the methane yields and kinetic production.

In our case, the AFW fraction is relatively low (0.7% for scenario 1 and 3.4% for scenario 2) which is expected not to negatively influence the AD process.

Figure 3 summarizes the annual flow diagram of the sludge and sludge mixed with AFW conversion into energy. It has been found that higher is the AFW amount, more important is the produced electricity. Moreover, significant reduction in the amounts of sludge and AFW after the AD process is also clear. The produced digestate is generally rich in nutrients and could be valorized in agriculture as a biofertilizer. However, before that, an in-depth physico-chemical characterization (especially its heavy metals and nutrients contents) is necessary to ensure its safe and optimal reuse.

Emissions Reduction Potential

According to the Intergovernmental Panel on Climate Change (IPPC), WWTPs contribute to the GHG emissions in the atmosphere during the wastewaters and sludge treatment and management [START_REF] Eggleston | IPCC Guidelines for National Greenhouse Gas Inventories[END_REF]. The carbon footprint represents the direct or indirect emissions of total emissions of CH4 and nitrous oxide (N2O) caused directly or indirectly by the WWTP. The direct GHG emissions are originated from biological processes during: (i) wastewaters collection, (ii) wastewaters treatment, and (iii) wastewaters discharge [START_REF] Parravicini | Greenhouse Gas Emissions from Wastewater Treatment Plants[END_REF]. Inside the Al-Russayl WTTP, the direct N2O emission could probably occur at three locations based on literature [START_REF] Parravicini | Greenhouse Gas Emissions from Wastewater Treatment Plants[END_REF][START_REF] Chai | Carbon Footprint Analyses of Mainstream Wastewater Treatment Technologies under Different Sludge Treatment Scenarios in China[END_REF]: the anoxic tank, the MBBR unit and in the receiving water body. However, the CH4 emission should occur mainly in the DAF and coagulation-flocculation unit, in the sludge dewatering step, in the sludge drying basin, and in the receiving water body [START_REF] Parravicini | Greenhouse Gas Emissions from Wastewater Treatment Plants[END_REF]. The indirect GHG emissions in WWTPs mainly include those related to the electricity supply and the sludge transportation to the landfill.

In our case, the carbon footprint due to direct emissions of GHG emissions of the Al-Russayl WWTP cannot be precisely estimated due to the availability of limited data concerning the wastewater quality progress in the treatment line. However, based on the literature, the direct N2O emission in the WWTPs could vary in a large range between 0.003% and 0.6% (Kg NO2-N/Kg total N (TN)) depending on the wastewaters loads and operating conditions [START_REF] Parravicini | Greenhouse Gas Emissions from Wastewater Treatment Plants[END_REF][START_REF] Law | Nitrous oxide emissions from wastewater treatment processes[END_REF]. Concerning the N2O emission in the water receiving body, it is generally fixed to 0.5% of the effluent TN content [START_REF] Eggleston | IPCC Guidelines for National Greenhouse Gas Inventories[END_REF]. Regarding CH4 emission, it is usually more complicated to be evaluated in comparison to NO2. However, for the whole

Emissions Reduction Potential

According to the Intergovernmental Panel on Climate Change (IPPC), WWTPs contribute to the GHG emissions in the atmosphere during the wastewaters and sludge treatment and management [START_REF] Eggleston | IPCC Guidelines for National Greenhouse Gas Inventories[END_REF]. The carbon footprint represents the direct or indirect emissions of total emissions of CH 4 and nitrous oxide (N 2 O) caused directly or indirectly by the WWTP. The direct GHG emissions are originated from biological processes during: (i) wastewaters collection, (ii) wastewaters treatment, and (iii) wastewaters discharge [START_REF] Parravicini | Greenhouse Gas Emissions from Wastewater Treatment Plants[END_REF]. Inside the Al-Russayl WTTP, the direct N 2 O emission could probably occur at three locations based on literature [START_REF] Parravicini | Greenhouse Gas Emissions from Wastewater Treatment Plants[END_REF][START_REF] Chai | Carbon Footprint Analyses of Mainstream Wastewater Treatment Technologies under Different Sludge Treatment Scenarios in China[END_REF]: the anoxic tank, the MBBR unit and in the receiving water body. However, the CH 4 emission should occur mainly in the DAF and coagulationflocculation unit, in the sludge dewatering step, in the sludge drying basin, and in the receiving water body [START_REF] Parravicini | Greenhouse Gas Emissions from Wastewater Treatment Plants[END_REF]. The indirect GHG emissions in WWTPs mainly include those related to the electricity supply and the sludge transportation to the landfill.

In our case, the carbon footprint due to direct emissions of GHG emissions of the Al-Russayl WWTP cannot be precisely estimated due to the availability of limited data concerning the wastewater quality progress in the treatment line. However, based on the literature, the direct N 2 O emission in the WWTPs could vary in a large range between 0.003% and 0.6% (Kg NO 2 -N/Kg total N (TN)) depending on the wastewaters loads and operating conditions [START_REF] Parravicini | Greenhouse Gas Emissions from Wastewater Treatment Plants[END_REF][START_REF] Law | Nitrous oxide emissions from wastewater treatment processes[END_REF]. Concerning the N 2 O emission in the water receiving body, it is generally fixed to 0.5% of the effluent TN content [START_REF] Eggleston | IPCC Guidelines for National Greenhouse Gas Inventories[END_REF]. Regarding CH 4 emission, it is usually more complicated to be evaluated in comparison to NO 2 . However, for the whole WWTP, it is generally up to 30% of the produced biogas [START_REF] Yoshida | Plant-integrated measurement of greenhouse gas emissions from a municipal wastewater treatment plant[END_REF]. In the receiving water bodies, the CH 4 emission is equal to 0.025 kg CH 4 /kg of chemical oxygen demand (COD) of the effluent [START_REF] Eggleston | IPCC Guidelines for National Greenhouse Gas Inventories[END_REF]. Regarding the sludge line, the CH 4 is emitted during: the storage and dewatering of the digested sludge and the heat and electricity production unit (non-burned methane) at percentages of 2-4.5%, and 1.3-1.8% of the total produced CH 4 amount [START_REF] Parravicini | Greenhouse Gas Emissions from Wastewater Treatment Plants[END_REF]. In the current study, we focused mainly on the avoided indirect GHG emissions (CO 2 equivalent amount) due to the AD of the sludge alone and mixed with AFW (Figure 3). Therefore, two indirect aspects have been considered: (i) the substitution of the used electricity from the national grid by the one produced from biogas, and (ii) the reduction of the sludge amount to be transported from Al-Russayl WWTP to the landfill by trucks. For a grid electricity emission factor of 0.858 tCO 2 MWh -1 [START_REF] Charabi | Strategic pathways and regulatory choices for effective GHG reduction in hydrocarbon based economy: Case of Oman[END_REF], the emissions avoidance potential per year and during the project lifetime by the electricity generation from Al-Russayl WWTP sludge only (scenario 1) was estimated to be about 1883 and 37,659 tCO 2 , respectively. The average annual and "total" reduced GHG emission reached about 2212; "44,235" and 3527; and "70,536" tCO 2 year -1 when the sludge was co-digested with 2.0 (scenario 2) and 10.0 (scenario 3) tonnes day -1 of AFW, respectively (Figure 4). The avoided GHG emissions due to fuel combustion during the sludge transportation to landfills were calculated for transporting trucks capacities of seven tonnes, a distance from the WWTP to the landfill of 50 km and a sludge transport factor of 0.113 kgCO 2 km -1 . They were estimated to only 66 tCO 2 year -1 for the three studied scenarios. This value is very low compared to those calculated when using the electricity generated by the biogas instead of the national grid. It is worth mentioning that the total GHG emission avoidance in the case of the WWTP of Al-Russayl remain relatively low compared to those calculated for larger WWTPs. For example, in South Columbus, USA, a net GHG emission reduction of 9600 tCO 2 year -1 is achieved through the co-digestion of sludge with fat, oils, grease, and co-generation heat and power [START_REF] Shen | An overview of biogas production and utilization at full-scale wastewater treatment plants (WWTPs) in the United States: Challenges and opportunities towards energy-neutral WWTPs[END_REF].

In Oman's case, it is essential to underline that stringent emission reduction policies and appropriate incentives for bioenergy can encourage the further adoption of biogas recovery from sludge and other organic-matter-rich-materials [START_REF] Edwards | A review of policy drivers and barriers for the use of anaerobic digestion in Europe, the United States and Australia[END_REF]. For instance, the European Union uses the "renewable energy directive (2018/2001/EU)" as an efficient framework for member countries to achieve CO 2 emission reduction targets. Bioenergy from anaerobic digestion of organic wastes (including sludge) is stimulated within this framework for further emissions reduction potential and environmental preservation [START_REF] Edwards | A review of policy drivers and barriers for the use of anaerobic digestion in Europe, the United States and Australia[END_REF].

were estimated to only 66 tCO2 year -1 for the three studied scenarios. This value is very low compared to those calculated when using the electricity generated by the biogas instead of the national grid. It is worth mentioning that the total GHG emission avoidance in the case of the WWTP of Al-Russayl remain relatively low compared to those calculated for larger WWTPs. For example, in South Columbus, USA, a net GHG emission reduction of 9600 tCO2 year -1 is achieved through the co-digestion of sludge with fat, oils, grease, and co-generation heat and power [START_REF] Shen | An overview of biogas production and utilization at full-scale wastewater treatment plants (WWTPs) in the United States: Challenges and opportunities towards energy-neutral WWTPs[END_REF]. In Oman's case, it is essential to underline that stringent emission reduction policies and appropriate incentives for bioenergy can encourage the further adoption of biogas recovery from sludge and other organic-matter-rich-materials [START_REF] Edwards | A review of policy drivers and barriers for the use of anaerobic digestion in Europe, the United States and Australia[END_REF]. For instance, the European Union uses the "renewable energy directive (2018/2001/EU)" as an efficient framework for member countries to achieve CO2 emission reduction targets. Bioenergy from

Economic Performance

The total digester cost and related operating and maintenance costs for the anaerobic digestion of the produced sludge in the studied WWTP were found to be $1.082 million by using Equation [START_REF] Gherghel | A review on wastewater sludge valorisation and its challenges in the context of circular economy[END_REF]. This cost increases to about $1.242 and $1.855 million for scenarios 2 and 3, respectively. On the other hand, the total electricity generation cost from methane was determined to be about $3.235, $3.800, and $6.060 million for scenarios 1, 2, and 3, respectively. It can be deduced that the cost of biogas conversion into energy is much higher than the one related to the digester implementation, operating, and maintenance cost.

Regarding the revenue of this project, it is mainly constituted by the generated electricity selling. The other items, such as the CER benefits from the avoided GHG emissions and transport fuels, were relatively low. For instance, for scenario 2 and 3, the selling benefits of produced electricity was evaluated to $7.115 and $11.345 million and counted for about 98.1% and 98.2% of the total benefits, respectively.

Considering the economic feasibility of the produced sludge and AFW in the industrial estate conversion into electricity, it can be seen from Figure 5 that the three studied scenarios were financially feasible as their calculated NPV values over the project lifetime were positive. For scenario 1 (biogas recovery from sludge alone), the NPV is estimated to $393,483 over the project lifetime with an IRR and PBP of 19.4% and seven years, respectively. The most excellent feasibility is offered by the biogas recovery from the co-digestion of the sludge and 10 tonnes day -1 of agri-food wastes (Scenario 3), where the NPV, the IRR, and PBP were assessed to be $851,876; 21.8% and six years, respectively (Figure 5 and Table 3).

scenarios were financially feasible as their calculated NPV values over the project lifetime were positive. For scenario 1 (biogas recovery from sludge alone), the NPV is estimated to $393,483 over the project lifetime with an IRR and PBP of 19.4% and seven years, respectively. The most excellent feasibility is offered by the biogas recovery from the codigestion of the sludge and 10 tonnes day -1 of agri-food wastes (Scenario 3), where the NPV, the IRR, and PBP were assessed to be $851,876; 21.8% and six years, respectively (Figure 5 and Table 3). It is essential to underline that it is complicated to compare these values to those found in the literature. Indeed, such operation's efficiency depends on the feedstock's nature and flow rate, the AD process conditions (primarily temperature and residence time), the size of the used digesters, and the efficiency of the methane conversion into electricity [START_REF] Shen | An overview of biogas production and utilization at full-scale wastewater treatment plants (WWTPs) in the United States: Challenges and opportunities towards energy-neutral WWTPs[END_REF][START_REF] Mohammed | Feasibility study for biogas integration into waste treatment plants in Ghana. Egypt[END_REF][START_REF] Alhammad | Feasibility Study for a Biogas Plant in Jordan[END_REF].

Sensitivity Analysis Results

Since this economic study was performed under particular assumptions, it is important to carry out a sensitivity analysis that considers market instability versus time and costs vary. The studied options (see Section 2.4) showed that all of them were economically feasible. Indeed, the corresponding NPV and IRR were positive and higher than 10%, respectively (Figure 6a,b and Table 4). Option 1, which assumes that the generated electricity will be sold to businesses at the same price currently applied by the Omani electricity distribution company (0.148 $US kWh -1 ) instead of 0.138 $US kWh -1 (baseline simulation), has significantly increased the NPV and IRR for all the studied scenarios. Indeed, the related calculated NPV and "IRR" reached $0.552, $0.667, and $1.148 million and "23.1%", "23.8%", and "26.0%" for scenario 1, 2, and 3, respectively (Table 3 and Figure 6a,b). The best option yielding the highest NPV and IRR corresponds to where the engaged costs were supposed to decrease by 15% (option 2). Under these conditions, the calculated NPV values were determined to be $0.706, $0.845, and $1.419 million for scenarios 1, 2, and 3, respectively. These values are 79.6%, 75.6%, and 66.5% higher than those found for the baseline option. Moreover, the IRR values were significantly higher than the current banking interest rates since they reached 30.1%, 31.0%, and 33.9% for options 1, 2, and 3, respectively. The PBP for the three scenarios were evaluated to 5 years only (Figure 6c).

On the other hand, even with a 15% increase in the calculated costs, the NPV and IRR are still positive and higher than 10%, respectively (Figure 6a,b, andTable 4). However, the related NPV has significantly decreased compared to the baseline option. They were assessed to be about $80,823, $116,793, and $285,047 for options 1, 2, and 3, respectively. The IRR values have also considerably decreased compared to the baseline condition, with values of only 11.7%, 12.2%, and 13.5% for options 1, 2, and 3, respectively. The PBP increased to 9 years for all the studied options (Figure 6c).

It is worth mentioning that the benefits of the digested sludge valorization as organic fertilizers instead of the commercial ones were not included in this study. This is attributed to the uncertainties related to the heavy metals concentrations progress versus time, especially cadmium and molybdenum. In this regard, Alhammad [START_REF] Alhammad | Feasibility Study for a Biogas Plant in Jordan[END_REF], when studying the economic feasibility of turning dairy manure farm (generated by 2000 cows) into electricity at Zarqa, Jordan, reported that the expected revenue from the annual production of organic fertilizer was to 24,000 €. It is 33% higher than the benefits derived from electrical energy generation. The best option yielding the highest NPV and IRR corresponds to where the engaged costs were supposed to decrease by 15% (option 2). Under these conditions, the calculated NPV values were determined to be $0.706, $0.845, and $1.419 million for scenarios 1, 2, and 3, respectively. These values are 79.6%, 75.6%, and 66.5% higher than those found for the baseline option. Moreover, the IRR values were significantly higher than the current banking interest rates since they reached 30.1%, 31.0%, and 33.9% for options 1, 2, and 3, respectively. The PBP for the three scenarios were evaluated to 5 years only (Figure 6c).

On the other hand, even with a 15% increase in the calculated costs, the NPV and IRR are still positive and higher than 10%, respectively (Figure 6a,b, and Table 4). However, the related NPV has significantly decreased compared to the baseline option. They were assessed to be about $80,823, $116,793, and $285,047 for options 1, 2, and 3, respectively. The IRR values have also considerably decreased compared to the baseline condition, with values of only 11.7%, 12.2%, and 13.5% for options 1, 2, and 3, respectively. The PBP increased to 9 years for all the studied options (Figure 6c).

It is worth mentioning that the benefits of the digested sludge valorization as organic of the commercial ones were not included in this study. This is attributed to the uncertainties related to the heavy metals concentrations progress versus time, especially cadmium and molybdenum. In this regard, Alhammad [START_REF] Alhammad | Feasibility Study for a Biogas Plant in Jordan[END_REF], when studying the economic feasibility of turning dairy manure farm (generated by 2000 cows) into electricity at Zarqa, Jordan, reported that the expected revenue from the annual production of organic fertilizer was to 24,000 €. It is 33% higher than the benefits derived from electrical energy generation.

On the other hand, it is essential to include in future investigations the social aspect that could include issues related to sludge' odors complaints, the public perception of renewable energy recovery from sludge, and the political support to such technology. Regulatory issues should also be considered in this context. They should emphasize the discrepancies between concerned governmental agencies, tariffs of generated electricity and interconnection with the national grid, and finally, the faced-challenges towards a full-respect of water and sludge discharge/reuse limits as well as air quality.

Finally, for a sustainable environment preservation, the production of sludge should be minimized as maximum as possible at its production source through the promotion of the following major tasks [START_REF] Collivignarelli | What Advanced Treatments Can Be Used to Minimize the Production of Sewage Sludge in WWTPs?[END_REF]: (i) adopting new processes in the wastewater treatment process, (ii) optimizing the dewatering processes for lower sludge water contents, and (iii) reducing the fraction of volatile solids through various oxidation methods.

Conclusions

This technical-environmental-economic feasibility shows a substantial potential for biogas and electricity recovery from the digestion of the sludge produced at the Al-Russayl industrial estate WWTP in Oman. Findings were promising when sludge was applied alone or in combination with agri-food wastes, respectively. The best results in terms of biogas production and electricity recovery were obtained in the scenario 3 (sludge mixed with 10 tonnes/day of AFW). In this scenario, significant methane amounts were recovered (more than 18 Mm 3 ) and converted into electricity (more than 82 GWh) for the whole project lifetime. This generated electricity is able to cover the overall current needs of the WWTP at this industrial estate. The in situ use of the produced electricity will enhance its energy security and will permit its sustainable functioning. Moreover, the project implementation will significantly reduce the GHG emissions (more than 70,000 tCO 2 ) mainly due to the used-generated electricity from biogas instead of the one supplied by the national grid network. The cost-benefit analysis shows that the co-digestion of WWTP sludge with agri-food wastes is particularly economically attractive with maximum NPV and IRR values of $851,876 and 21.8%, respectively, and a payback period of six years. The sensitivity analysis demonstrates that the NPV and IRR values reached $1,418,704 and 34.0% when the total expenses were reduced by 15%. However, when the total engaged expenses were increased by 15%, the NPV and IRR values considerably decreased, but they were still positive and slightly higher than 10%, respectively.

The in-depth physico-chemical characterization of the sludge and the agri-food wastes produced in the Al-Russayl industrial estate is an essential task for the future updating and exploitation of this feasibility study. This characterization will mainly concern mainly their total solid and volatile matter contents, their potential degradability rate, and their calorific energy potential.

The application of such a process in other existing WWTPs and future planned ones will permit Oman to achieve the sustainable goals for low GHG emissions, sanitation, and water resources protection. A thorough assessment of the techno-environment-economic feasibility of biogas production from the co-digestion of sludge and agri-food wastes in the planned WWTP will enable the government to implement new sustainable and environmental-friendly plants. These plants should integrate the biogas recovery and conversion into electricity and the agronomic valorization of the generated digestate, which are essential steps towards circular economy concept application and sustainability.

Figure 1 .

 1 Figure 1. The design and main operating conditions of Al-Russayl wastewater treatment plant. (DAF: dissolved air flotation; MBBR: Moving bed bioreactor).

Figure 1 .

 1 Figure 1. The design and main operating conditions of Al-Russayl wastewater treatment plant. (DAF: dissolved air flotation; MBBR: Moving bed bioreactor).

- 1 ) 4 Initial

 14 , dry basis-Scenario 2 0.4 This study, baseline option Annual increase of AFW used flow rate (%) 2.0 Average annual dry AFW flow rate (2021-2040) (m 3 year -1 )-Scenario 2 177.AFW flow rate (2021) (tonnes day -1 ), wet basis-Scenario 3 10.0 Initial AFW flow rate (2021) (tonnes day -1 ), dry basis-Scenario 3 2.0 Average annual dry AFW flow rate (2021-2040) (m 3 year -1 )-Scenario 3 886.9

Figure 2 .

 2 Figure 2. Biogas, methane, and electricity generation capacities during the lifetime project by the digestion of sewage sludge alone (SS) and its co-digestion with agri-food wastes (AFW) (Scenario 1: SS alone; Scenario 2: SS+ 2 tonnes day -1 of AFW; Scenario 3: SS+ 10 tonnes day -1 of AFW).

Sustainability 2021 , 20 Figure 3 .

 2021203 Figure 3. Average annual flow diagram of the conversion of sludge and AFW into energy (WWTP: wastewater treatment plant; Sc: Scenario where Sc1: SS alone; Sc2: SS+ 2 tonnes day -1 of AFW; Sc3: SS+ 10 tonnes day -1 of AFW).

Figure 3 .

 3 Figure 3. Average annual flow diagram of the conversion of sludge and AFW into energy (WWTP: wastewater treatment plant; Sc: Scenario where Sc1: SS alone; Sc2: SS+ 2 tonnes day -1 of AFW; Sc3: SS+ 10 tonnes day -1 of AFW).

Figure 4 .

 4 Figure 4. CO2 emission reduction potential during the lifetime of project by the digestion of sewage sludge (SS) alone and its co-digestion with agri-food wastes (AFW) (Scenario 1: SS alone; Scenario 2: SS+ 2 tonnes day -1 of AFW; Scenario 3: SS+ 10 tonnes day -1 of AFW).

Figure 4 .

 4 Figure 4. CO 2 emission reduction potential during the lifetime of project by the digestion of sewage sludge (SS) alone and its co-digestion with agri-food wastes (AFW) (Scenario 1: SS alone; Scenario 2: SS+ 2 tonnes day -1 of AFW; Scenario 3: SS+ 10 tonnes day -1 of AFW).

Figure 5 .

 5 Figure 5. Calculated net present value (NPV) and internal return rate (IRR) of the Al-Russayl WWTP sewage sludge (SS) digestion or co-digestion with agri-food wastes (AFW) project for the baseline conditions (Scenario 1: SS alone; Scenario 2: SS+ 2 tonnes day -1 of AFW; Scenario 3: SS+ 10 tonnes day -1 of AFW).

Figure 6 .

 6 Figure 6. Cont.

Figure 6 .

 6 Figure 6. Economic feasibility of electricity production from Al-Russayl WWTP sludge and agri-food wastes co-digestion process. Sensitivity study effects on Net present value (a), Internal return rate (b), and Payback period (c) (Scenario 1: SS alone; Scenario 2: SS+ 2 tonnes day -1 of AFW; Scenario 3: SS+ 10 tonnes day -1 of AFW; Baseline conditions: electricity selling price = $0.138 kwh -1 ; Option 1: electricity selling price = $0.148 kwh -1 ; Option 2: baseline conditions+ annual expenses decrease by 15%; Option 3: Baseline + annual expenses increase by 15%).

Figure 6 .

 6 Figure 6. Economic feasibility of electricity production from Al-Russayl WWTP sludge and agri-food wastes co-digestion process. Sensitivity study effects on Net present value (a), Internal return rate (b), and Payback period (c) (Scenario 1: SS alone; Scenario 2: SS+ 2 tonnes day -1 of AFW; Scenario 3: SS+ 10 tonnes day -1 of AFW; Baseline conditions: electricity selling price = $0.138 kwh -1 ; Option 1: electricity selling price = $0.148 kwh -1 ; Option 2: baseline conditions+ annual expenses decrease by 15%; Option 3: Baseline + annual expenses increase by 15%).

Table 1 .

 1 Main technical, environmental, and economic assumptions and indicators considered for sludge conversion into energy in the WWTP of Al Russayl industrial estate (AFW: Agri-food wastes).

	Biogas Generation

Average annual dry sludge flow rate (2021-2040) (m 3 year -1 )-Scenario 1 3724.8 This study, baseline option Density of thickened sludge (kg m -3

Table 2 .

 2 Heavy metals contents in the used sludge in comparison with the standards for sludge reuse in agriculture in Oman (according to 145/93 ministerial decision) and Europe (European directive 86/278/EEC).

				Ratio (Omani
	Metal	Content (mg kg -1 )	Omani Standard	Stan-dard/Measured	European Standard
				Content)
	Arsenic	<4	-	-	-
	Boron	20	-	-	-
	Barium	49	-	-	-
	Cadmium	<4	20	-	20-40
	Cobalt	2	-	-	-
	Chromium	190	1000	5.3	-
	Copper	280	1000	3.6	1000-1750
	Mercury	0.1	10	100	16-25
	Manganese	210	-	-	-
	Molybdenum	36	20	0.6	-
	Nickel	29	300	10.3	300-400
	Lead	90	1000	11.1	750-1200
	Antimony	<7	-	-	-
	Selenium	<2	50	-	-
	Vanadium	12	-	-	-
	Zinc	270	3000	11.1	2500-4000
	Total cyanide	<0.5	-	-	-
	Fluorides	<500	-	-	-

Table 3 .

 3 Annual and project lifetime (20 years) biogas, methane, and electricity produced amounts from the digestion of Al Russayl WWTP sludge or its co-digestion with agri-food wastes (Scenario 1: SS alone; Scenario 2: SS+ 2 tonnes day -1 of AFW; Scenario 3: SS+ 10 tonnes day -1 of AFW).

	Scenario 1	Scenario 2	Scenario 3

year 0.754 Mm 3 /year 1.413 Mm 3 /year 3028.2 T/year 3258.7 T/year 2.2 GWh/year 2.6 GWh/year 4.1 GWh/year Methane conversion into electricity Reuse in the WWTP 874.0 T/year 1352.9 T/year 2970.5 T/year

	Agri-food Wastes	886.9 T/year of AFW: Sc3 177.4 T/year		754.3	Biogas	0.886 Mm 3 /	Biogas storage
	(AFW)	of AFW: Sc2	Mixing tank	T/year
		0.0 T/year
		of AFW: Sc1
	+				Digester
	3724.8			Mesophilic anaerobic digestion
	T/year of SS
	Sewage
	Sludge (SS)				Digestate tank

Table 4 .

 4 Economic feasibility of biogas generation from Al-Russayl WWTP sludge and agri-food wastes co-digestion.

	NPV ($ Million)	IRR (%)	PBP

Sensitivity study results (Scenario 1: SS alone; Scenario 2: SS+ 2 tonnes day -1 of AFW; Scenario 3: SS+ 10 tonnes day -1 of AFW; NPV: net present value; IRR: internal return rate; PBP: payback period).

Data Availability Statement: Data available on request.

Acknowledgments: Authors would like to thank Lokman Zaibet for his technical and scientific support.

Conflicts of Interest:

The authors declare no conflict of interest.


Trong Trung Le

Zarel Valdez-Nava

Sombel Diaham
email: sombel.diaham@laplace.univ-tlse.fr

Dielectrophoretic Chain Assembly of BaTiO 3 Particles in Silicone Gel Composites

Composite insulating materials with enhanced dielectric permittivity, like silicone gel with barium titanate particles (BaTiO3) are promising candidates in the context of advanced field grading encapsulants for power electronic applications. The recent developments of field-assisted assembly techniques for particle structuration in polymeric matrix enable to obtain anisotropic material properties in the direction where it is the most suitable. This approach allows going beyond some composite intrinsic limitations and paves new ways to improve insulating materials to reach higher voltage performances at power system level. This paper aims to present the effect of dielectrophoretic electric field waveform and frequency on the anisotropic structuration of BaTiO3 particles in silicone gel and to report on the impact of these parameters on the chain formation.

I. INTRODUCTION

The acceleration of climate change pushes us to reduce of greenhouse gas emissions. As a result, faster development of transport electrification as well as greener energy production must continue. This will not be achievable without a significant improvement in the electrical insulation to enable the operating voltage increase in most of the power conversion systems. SiC and GaN wide bandgap semi-conductor power devices with higher operating electric field are becoming readily available and they might be a more efficient alternative for replacing the conventional silicon IGBTs with their advantages of faster switching speed, higher operating temperature, lower conduction resistance and especially a higher working voltage capability [START_REF]SiC & GaN Power Semiconductors Report -2021[END_REF]. With increasing the voltage rating in power modules, the encapsulation materials used like silicone gel can be more easily subjected to electrical degradations (i.e. partial discharges, electrical treeing, breakdown) due to higher localized electrical field at triple points [START_REF] Bayer | Simulation of the electric field strength in the vicinity of metallization edges on dielectric substrates[END_REF] [START_REF] Han | Electrical Tree Initiation and Growth in Silicone Rubber under Combined DC-Pulse Voltage[END_REF]. To figure out such issues, current researches in the field have seen a rise in the development of functionnaly graded or anisotropic polymer composites with field grading properties. The obtained composites present adjusted dielectric properties acting as electrical constraint spreader within the insulation. This might participate to improve the overall reliability by mitigating strong localized electric fields. As homogeneously-mixed polymer composites can present some limitation due to the filler content it is reasonably possible to add to the matrix, the dielectric properties can flatten accordingly [START_REF] Ham | Electrical Properties of SrTiO3epoxy Composite Thick Films on Cu Plate PCB substrates[END_REF] [START_REF] Kume | High-Thermal-Conductivity AlN Filler for Polymer/Ceramics Composites[END_REF]. In order to overcome this limitation, the composite filler architecture can be modified by using specific 3D electric field assembly techniques that enable to increase the composite dielectric properties.(e.g. its permittivity). The strength of this approach is to allow to structure the composites directly in-situ within the system to isolate by using the different metal electrodes and without modifying the design or the layout [START_REF] Diaham | Field Grading Composites Tailored by Electrophoresis -Part 1: Principle and Permittivity Gradient in Uniform Electric Field[END_REF] [START_REF] Diaham | Field Grading Composites Tailored by Electrophoresis-Part 3: Application to Power Electronics Modules Encapsulation[END_REF]. In some of the embodiments to apply the electric field during the composite assembly, particles can spatially arrange each other around the sharp electrodes to lower the local electrical field by acting as an electrical stress-control or field grading material (FGM).

An alternative approach consists in the possibility to structure the particles dielectrophoretically in a "pearl chain" fashion way between the system electrodes to favor the anisotropy of the properties. Famous examples have reported composites with enhanced thermal [START_REF] Hone | Thermal conductivity of single-walled carbon nanotubes[END_REF][9] or electrical conduction [START_REF] Kane | Temperature-dependent resistivity of single-wall carbon nanotubes[END_REF] [START_REF] Mohan | Graphene-based materials and their composites: A review on production, applications and product limitations[END_REF]. The use of anisotropic composites can efficiently improve a property in one specific direction or obtain the same property with a lower initial filler content [START_REF] Wang | Computational study of filler microstructure and effective property relations in dielectric composites[END_REF] [START_REF] Belijar | Particle chain formation in a liquid polymer under ac electric field: Model and experiments[END_REF].

Despite various papers have reported particle chain assemblies under dielectrophoretic field in epoxy resin [START_REF] Belijar | Dielectric breakdown of high-k epoxy-based anisotropic composites[END_REF] [START_REF] Park | Electric-field-induced ordering and pattern formation in colloidal suspensions[END_REF], studies in softer materials like silicone gel used as encapsulation in power modules are more rare. More specifically, this paper presents some guideline for structuring anisotropic insulating polymer composites using dielectrophoresis with a various electrical and temporal parameters (e.g. frequency, waveform, time).

II. EXPERIMENTAL PART

A. Materials and Sample Preparation

The matrix used in this study is a two-components SilGel® 612 (A:B 1:1) from Wacker with a room temperature vulcanization reaction. The mixture of part A and part B has a density of 0.97 g/cm 3 and a viscosity of 1000 mPa/s. The curing is achieved by a crosslinking process, initiated by mixing the two components and occurs by condensation with addition reaction of platinum catalyst (part B). The final silicone gel is obtained after 150 min at room temperature. It is optically fully transparent before and after curing which is especially important to observe the particle chaining by transmission microscopy and to check structuration. Barium titanate (BaTiO3) particles with a density of 5.997±0.0181 g/cm 3 were added at 1 vol% for all the experiments and were mixed in a planetary mixer under primary vacuum. The polyhedral-shaped particles have an average diameter of 462 nm. Because of the short pot life of the mixture, all the dielectrophoretic structuration have been realized just after the mixing. One hour after the mixing, the viscosity rapidly increases ending by freezing the structure permanently.

B. Dielectrophoretic experiments with optical observation

Dielectrophoresis (DEP) structuration is based on applying an electric field between two parallel electrodes filled in with the mixture of silicone gel with the BaTiO3 particles. For the process optimization, two parallel copper electrodes with a gap of 0.5 mm using insulating spacer were used. The two electrodes were glued on a glass slide by using a transparent epoxy resin, as shown in Fig. 1. To ensure the highest observation quality, the mixture was poured up to half the height of the spacer to avoid parasitic optical meniscus induced by the DEP forces at the electrode edges,. Transmission light coming from backside of the sample cell was used to get a better contrast for particle chain observation.

Particle chaining was performed under DC, AC sine wave and bipolar square wave in a large frequency range. In DC, the voltage was applied using a Keithley SMU 2410 at an electric field of 500 V/mm. Both for AC sine and square wave experiments, the voltage was applied using a HV amplifier controlled by a function generator. The voltage was set at 500 Vpp/mm with frequency ranging from 10 mHz to 1 kHz. The maximum time of each experiment was 30 minutes because of the late movements of the particles after 25 minutes. Real-time observation was realized with a Keyence VH-Z500R microscope.

III. RESULTS AND DISCUSSION

A. Particle Chaining in Silicone Gel in AC Sine Wave

The result of optical observation of a compound under a sinusoidal electric field at a frequency of 1 Hz is presented in Fig. 2. Firstly, this confirms the structuration of particle chain starts immediately when the electric field is applied. However, and more surprisingly, after the BaTiO3 particles start chaining parallel to applied the electric field, then, they start sidely stacking to take the form of larger columns aligned with the electric field. The length of the chains can reach the 500 µm electrode gap spacing only after 8 s in these experimental conditions. Some of the chains appear as not perfectly aligned in the direction of the applied electric field because of the lateral dielectric interactions with their closest chain neighbor when they grow. Simultaneously with the evolution of the length, the number of chains is increased too. After 20 s, all the chains has reached their maximum length. From this stage, only lateral chain column movements are observed. This result is effectively in agreement with previous study [START_REF] Belijar | Particle chain formation in a liquid polymer under ac electric field: Model and experiments[END_REF]. When particles are closer to each other, the local volume fraction increases consequently, leading to stronger dielectrophoretic force. Increasing in dielectrophoretic force leads to the assembly of particles and makes the columns to stack laterally.

B. Influence of Frequency

Chain formation depends not only from DEP forces, but also from complex electro-hydrodynamic phenomena that is triggered by charge transport along the volume of the composite material in liquid state. Phenomena are in competition as the former creates the pearl-like particle chains from near-range movements of the particles in suspension, and the later induces the displacement of the liquid and particles in the full volume of the sample. It is known that the change in applied frequency can modify the equilibrium of these two phenomena to favor particle-chain formation or to 'break' or avoid the arrangement [START_REF] Belijar | Particle chain formation in a liquid polymer under ac electric field: Model and experiments[END_REF]. In the studied frequency range, 10 mHz to 1 kHz, we observe that frequency has an important influence in the structure and kinetics of chain formation. In Fig. 3, we can observe very large difference in the structures of the particle chains obtained when applying 1 kHz and 10 mHz, after 2 mins and 30mins.

Under high frequency (1 kHz), first, the chains form in the direction of field, with many chains being formed within the In low frequency (10 mHz), chains form also during the application of a half-cycle. However, every time the polarity is reversed in the next half-cycle, the movement of the liquid and particles break the chains partially. This leads to a very large difference of the structure, where at 1 kHz frequency, the final structure has longer and narrower chains when compared to a structure obtained from the application of 10 mHz (Fig. 3). This partial breakup of the chains on each alternance of the low-frequency field, leads to a twofold result: a subset of isolated chains with very short length (< 20 µm), and other chains that are composed of many laterally-stacked chains as a result of the coalescence of short chains under DEP forces.

Video analysis allowed to track individual chains and chaining times. Figure 4 shows a plot of the time required to produce a chain of length of 500 µm. This time has a minimum for an applied frequency of 1 Hz. . From DC to 1 Hz, the electro-hydrodynamic phenomena (EHD) is limiting the formation of particle chains, following the general tendency observed by other studies [START_REF] Belijar | Particle chain formation in a liquid polymer under ac electric field: Model and experiments[END_REF]. As the influence of the EHD phenomena further decreases above 1 Hz, unexpectedly, the chain growth time to reach 500µm increases from 8 s to 35 s at 1 kHz. This could possibly mean that the DEP force is decreasing as frequency increases for the particles contributing to the formation of the observed chain. The DEP force is described by Eq. 1 as follows:

(1) Where em is the particles permittivity, R is particles radius, E the electric field magnitude and K is the Clausius-Mossoti factor that can be analytically written as:

(2) where ep is the particles permittivity.

Two possible explanations are proposed. One would imply that the Clausius-Mossoti factor changes as the particle and/or liquid silicon-based matrix permittivities change as a frequency is increasing. The other possibility is that, if we consider that K remains constant, and with less impact of the EHD forces against chain formation, the chain formation rate increases in the full sample. This would imply that by observing a single chain, the time required to reach a certain length will depend on the total DEP force acting on the particles that are forming it but also on the availability of such particles. If the availability of the particles is reduced, i.e. as many are already part of another chain, the overall rate of growth for a given chain can be reduced.

If we observe the total time required for the full formation of the chained structure, at different frequencies (Fig. 5), it can be noted that the time decreases as frequency increases. The values fit well with a logarit form with f is frenquency applied:

tstable= -88log(f) + 575 (3) After this time, no further particle movement is observed, reaching a 'stable' structure. This comforts the latest hypothesis proposed in the previous paragraph. Further insight on the impact of frequency and waveform to the structure was possible by making an image analysis of the final structured composites, after 30 min of field application. First, gray-scale images were processed to obtain binary images adapted to image processing. Then, the binary images were analyzed to estimate the ratio (chain density) of the surface occupied by the chains (black) in respect to the remaining matrix (white) surface (Fig. 6). It is to note that the transmitted light intensity through the sample will depend on the light interaction with the particles and chains. The resulting image sharpness and brightness will depend, among other parameters, on the particle size, inter-particle distance and depth within the sample. So, it is possible to estimate ratios well above the particle content. However, when comparing samples of equal volume fraction of particles, images will provide an indication of both the chain length and chain width. This chain density is reported in Fig. 7 for all studied frequencies (10 mHz to 1 kHz) and for the different applied waveforms (sine and square). Chain density increases with the applied electric field frequency and, when comparing the waveforms, the sinewave results have a slight increase of the chain density compared to the samples where a square waveform was applied.

IV. CONCLUSION

In the present work an anisotropic composite was elaborated by electric field-assisted assembly based on dielectrophoretic phenomena. High permittivity BaTiO3 particle chains were structured in a silicon gel insulating matrix.

When increasing the frequency from DC to 1 kHz, the particle chain formation rate follows the increase of the frequency as the electro-hydrodynamical phenomena is reduced with increasing frequency. The observed structuring kinetics and final particle chain density can help to tailor the processing conditions and the final properties of the anisotropic composites in an electrical insulation system.

Further studies are needed to understand the impact of the frequency and waveforms on to the electrical properties of the structured anisotropic composites.

Fig. 1 .

 1 Fig. 1. Experimental setup of particle chain dielectrophoretic assembly under optical microscope observation.

Fig. 2 .

 2 Fig. 2. Optical microscopy images with the evolution of chain formation under an AC sine field of 500 Vpp/mm at 1 Hz.

  volume of the material. The chains continue to grow until all particles are incorporated to the chains.

Fig. 3 .

 3 Fig. 3. Comparison of chain formation under a sinusoidal field of 500 Vpp/mm at frequencies of 1 kHz and 10 mHz and after 2 min and 30 min.

Fig. 4 .

 4 Fig.[START_REF] Ham | Electrical Properties of SrTiO3epoxy Composite Thick Films on Cu Plate PCB substrates[END_REF]. Time required for a single particle chain to reach 500 µm (the distance between electrodes) at different frequencies.

Fig. 5 .

 5 Fig.5. Time required to reach a stable state, with no apparent particle movement during sample structuring.

Fig. 6 .

 6 Fig.6. Image processing to obtain the chain density, i) count the number of chains and their with, ii) conversion of the gray-scale image to a binary format.

Fig. 7 .

 7 Fig. 7. Chain density after 30 min under sinusoidal, square waveforms with different frequency and DC fields.

ACKNOWLEDGEMENTS

The authors would like to thank the French National Research Agency (ANR) for funding this research through the FASTER-3D project (grant N° ANR-18-CE05-0005).