"Selection of Sustainable Raw Materials for Effective Product Optimization Using Applied Linear Techniques"

There is currently a global trend toward selecting raw
materials based on sustainable waste criteria and developing
sustainable, low energy consumption production...

ated. However, increasing the utilisation of biomass within the supply chain has the unfortunate effect of increasing the complexity of the supply chain as a result of the distributed nature of the energy source. Hydrogen has great potential as a fuel in the future. This is because of its clean combustion without generating greenhouse gases and CO 2 . It is inevitable that CO 2 is produced during the production of hydrogen, but with CO 2 capture technology, it is a clean fuel. Furthermore, the advantage of using hydrogen is increased when it is produced from renewable sources. Hydrogen can be produced directly from such biomass sources as wood [6] or molasses [7], or by directly using electric energy generated from solar or wind sources [8]. Wan Alwi and Abd Manan [9] proposed a simultaneous Process Integration strategy for energy targeting, placement of utilities with flue gas, and design of heat recovery networks.
Pan et al. [10] presented new insights into heat transfer intensified technologies for Heat Exchanger Network retrofits.
Their paper reports on a method to improve heat recovery during Heat Exchanger Network retrofits using heat transfer intensification, while accounting for pressure drop constraints and fouling mitigation. Oluleye et al. [11] developed a methodology to identify the potential for waste heat recovery in process sites.
They consider the temperature and quantity of waste heat sources from site processes and the site utility system. Sun et al. [12] demonstrated the complexity of costing steam for complex utility systems. It shows that true steam cost can only be evaluated by an optimisation model of the whole utility system. Process Integration analysis can be extended with some economic-environmental implications for an innovative environmentally friendly recovery and pre-treatment process [13]. Pan et al. [14] presented new insight into the application of energy efficient technologies in retrofitting natural gas combined cycle power plants with CO 2 capture unit.
They proposed optimal retrofitting strategies to minimise the efficiency penalty caused by integrating carbon capture units into the power plant Bassani et al. [15] described a multi-scale, multiphase and multi-component coal gasification system using detailed kinetic mechanisms for coal pyrolysis, char heterogeneous reactions and successive gas-phase reactions of the novel Acid Gas to Syngas (AG2S™) technology. This technology allows for reductions in the environmental impact of coal uses and improves the yield of coal gasification via reduction potential of H 2 S with CO 2 molecule.
Budzianowski et al. [16] presented a Total Chain Integration of sustainable biorefinery systems with special attention to state-ofart software tools for biorefinery integration. Kostevšek et al. [17] presented the concept of an ecosystem model that could be used as a tool for developing sustainable municipal energy systems.
Their ecosystem model combines analysis, optimisation and simulation of energy systems. Zeng et al. [18] performed steady state integrated natural gas and electric power system with bidirectional energy conversion. Klemeš et al. [19]

Applied Linear Technique
In a world with limited resources and serious environmental damage, it is obvious that more sustainable raw materials should be used for more effective product production. We must use materials that reduce environmental pollution, recycle waste and choose cleaner production processes. Fossil raw materials should be replaced by sustainable alternative raw materials such as biogas, waste wood, and municipal solid waste. Thermal conversion of Municipal Solid Waste (MSW) uses heat energy to reduce the volume of MSW and generate biofuels such as syngas, char and biooil. Typical thermal conversion technologies include incineration, pyrolysis and gasification.
Biochemical conversion of MSW uses enzymes and microorganisms to break down organics for biogas production and to produce value-added products. Biochemical conversion processes include anaerobic digestion, fermentation and composting. The applied linear technique is a thermodynamic method for evaluating different raw materials for different product production. Fossil raw materials can be replaced with sustainable alternatives such as biogas, waste wood, and municipal solid waste, following the determination of factors of raw material flow rate for different product production (f raw,prod ) using optimal production conditions. The optimal production condition for different raw materials can be calculated before the ratio factors of raw material determination by using the Aspen Plus simulator. The selection of different raw materials can be based on easy nonmathematical or mathematical Nonlinear Programming (NLP) and Mixed Integer Nonlinear  (Figures 1 & 2). The conversion of a specific product is equal to the specific basic component of different raw materials. The different product conversions can be determined by using reaction kinetics. Different product productions are presented with equations depending on the basic components from raw materials. This technique can be used to analyse the effectiveness of products and by-products production. Applied linear techniques is appropriate for retrofit. (Figure 2) The product molar flow rates (F prod,comp,raw ) can be determined by using a linear function, depending on the basic component of raw material molar flow rates (F comp,raw, prod ) and the factors of raw materials for different product production (f raw, prod ; Eq. 1). k prod,comp,raw presents the slope of lines, which is the same as the conversion of specific product production from specific basic components of different raw materials, calculating from reaction kinetics:  F prod,comp,raw = k prod,comp,raw ⋅ F comp,raw, prod ⋅ f raw, prod (1) Where subscript prod presents all product production (prod = 1 …N prod ) Where subscript comp represents all basic components of raw materials (comp = 1 …N comp ) Where subscript raw represents all different raw materials The basic components can be arranged for 1 mol during reaction. The total basic component of different raw material molar flow rate (TF comp ) for all possible products production is: The total specific product molar flow rate from different raw materials (TF prod ) is: The total specific product molar flow rate (TF prod ) is limited with minimal and maximal operation capacity (OCprod,min, OCprod,max; Eq.4). The basic components of raw material molar flow rates for different product production (F comp,raw,prod ) are limited by available minimal and maximal raw materials (RMcomp,raw,min, RMcomp.raw,max, Eq. 5): The basic components of raw material molar flow rates for different product production (F comp,raw, prod ) can be calculated using the raw material molar flow rates (F raw ) and their conversion (X comp,raw ): (6) This model could be used to select possible different product production from different fractions of raw materials (f raw ).
The total sum of factors for different raw materials (f raw, ) is equal to one: The factors of different raw materials (f raw, ) is equal to the ratio between specific (F raw ) and total raw material molar flow rate (ΣF raw ; raw = 1 …N raw ): The objective function (OBF; Eqs. 10) is maximised for additional profit of the retrofit. The additional income accounting for additional product production depends on the price of products (C prod). The additional cost includes the cost of raw materials and environmental impact ( C raw ), using 8000 operation hours (O) per year: This technique can very quickly calculate the perspective of specific raw materials for different product production by using the perspective factor (pf raw, prod ). A higher value of the perspective factor is more desirable. The perspective factor is the ratio between income and cost of each specific raw material for different product production: Different raw materials for different products can be easily : which can be modelled using the constraint: Low⋅ y ≤ x ≤ Up⋅ y where Low is the lowest value and Up is the highest value of the parameters.
F prod,comp,raw ≥ Low prod,comp,raw ⋅ y prod comp = 1 …N comp raw = 1 …N raw (13) F prod,comp,raw ≤ Up prod,comp,raw ⋅ y prod comp = 1 …N comp raw = 1 …N raw (14) Case study The applied linear technique is a very simple method that was tested without mathematical programming and NLP algorithms for existing methanol production (Chapter 3.3.1). Existing methanol production could be simply enlarged for 5% DME (dimethyl ether) production without modified process parameters, including additional separation within the first column (Chapter 3.3.2). For total replacement of methanol with DME production, the catalyst within the reactor would be changed (Chapter 3.2; this was not done).

Exsiting Methanol Production
The methanol process (Figure 3) is  Indirect DME production DME is produced via the catalytic dehydration of methanol over an amorphous alumina catalyst treated with 10.2% silica. A methanol conversion of about 80% is achieved within the reactor [28]. DME is produced by the following reaction: The catalytic dehydration of pure, gaseous methanol is carried out in a fixed-bed reactor. The product is cooled over two stages and subsequently distilled to yield pure DME. Small amounts of DME are recovered from the off-gas in a scrubber, and re-cycled to the reactor. The non-reactive methanol is separated from the water in a second column, and also recycled.

Applied Linear Technique for Methanol Production
The applied linear technique is a very simple method that can be solved without mathematical programming and with the NLP algorithm during existing methanol production using equations 1 to 11. Methanol can be produced from different raw materials that can be chosen in the neighbourhood between (Table 1 & Figure 4 limited to 5,000 kg/h using the following reaction: Figure 4) The basic components of raw material molar flow rates (F comp,raw, prod ) were CO and CO 2 for methanol production. The simulated F comp,raw, prod are presented in Table 1, given by the Aspen plus simulator during optimal conditions of 900 o C and 9 bar for 10,000 kg/h using different raw materials. (Table 1   The methanol molar flow rates (F MeOH,comp,raw ) can be determined by using a linear function, depending on the basic components of raw material molar flow rates (F comp,raw,MeOH ) and the factors of raw materials (f raw,MeOH ; using Eq. 1). k MeOH,CO,RAW for methanol production from CO was 65% using all raw materials (Figure 5a). k MeOH,CO2,RAW for methanol production from CO 2 was 30% using all raw materials ( Figure 5b): The sum of all basic components (comp=CO,CO 2 ) for different raw material molar flow rate in methanol production (TCF raw ) was: The factors of different raw materials for methanol production (f raw,MeOH ) was equal to the ratio between specific (TCF raw ) and total raw material molar flow rate (ΣTCF raw ; raw = 1 …Nraw; using Eq. 9): The total methanol product molar flow rate of different raw materials (TF MeOH ; using Eq. 3) was: The objective function (OBF; using Eqs. 10) was maximised for the additional profit of the retrofit. The additional income accounting for additional product production depends on the price of methanol products (C MeOH = 4EUR/kmol). The additional cost includes the cost of raw materials and environmental impact ( C raw , .37 MEUR/a ˗ 3.61 MEUR/a = 5.76 MEUR/a (37) The optimal factors of raw materials for methanol production were The most promising raw material was municipal solid waste.
The different raw materials for methanol production can be easily selected without mathematical algorithms by using the perspective factor. The selection solution was close to the optimum.

Applied Linear Technique for Methanol and DME Production
The applied linear technique is a very simple method for calculating, without mathematical programming and with the NLP algorithm, the requirements of existing methanol and DME (dimethyl ether) production. During existing methanol production, DME could be simply produced at a rate of up to 5% using the following reaction: In this case, the same raw materials (Table 1) were used as for methanol production. The mathematical model was very similar to that for methanol production, using Eqs. 15˗26 and including the additional equations for DME production, Eqs. 42˗61. The basic component of raw material molar flow rates (F CO,raw, DME ) was CO for DME production under optimal conditions of 900 o C and 9 bar.
During DME production, (TF DME ) was used as the maximal limit of DME capacity (OCDME,max=14.6 kmol/h): The DME molar flow rates (F DME,comp,raw ) can be determined by using the linear function, depending on the basic component of raw material molar flow rates (F comp,raw,DME ) and the factor of raw materials (f raw,DME ). k DME,CO,RAW for DME production from CO was 5% using all raw materials: F DME,CO,NG = k DME,CO,RAW ⋅ F CO,NG,DME ⋅ f NG,DME (43) F DME,CO,BG = k DME,CO,RAW ⋅ F CO,BG,DME ⋅ f BG,DME (44) F DME,CO,WW = k DME,CO,RAW ⋅ F CO,WW,DME ⋅ f WW,DME (45) F DME,CO,MSW = k DME,CO,RAW ⋅ F CO,MSW,DME ⋅ f MWS,DME ( The total sum of factors for different raw materials using methanol (f raw,Meoh ) and DME production (f raw,DME ) was equal to one: The factors for different raw materials using methanol (f raw,Meoh ) and DME production (f raw,DME ) were: The sum of all basic components (comp=CO, CO 2 ) for different raw material molar flow rate using methanol and DME production (TCF raw ) was: The factors of different raw materials for methanol and DME production (f raw,prod ) were equal to the ratio between specific (TCF raw ) and total raw material molar flow rate (ΣTCF raw ; raw = 1 …N raw ): The total methanol product molar flow rate from different raw materials (TF MeOH ) can be calculated using Eq. 36, and for DME was: TF DME = F DMECO,NG + F DME,CO,BG + F DME,CO,WW + F DME,CO,MSW The objective function (OBF; using Eqs. 10) was maximised for the additional profit of the retrofit. The additional income accounting for additional product production depends on the price of methanol and DME products (C MeOH =4EUR/kmol; C DME =5.5EUR/ kmol). The additional cost includes the cost of raw materials and environmental impact ( C raw , .55 MEUR/a ˗ 3.61 MEUR/a = 5.94 MEUR/a (61) The optimal factors of raw materials for methanol and DME productions were f NG :f BG :f WW :f MSW = 0.1:0.1:0.3:0.5, the same as for only methanol production. The optimal selection was dependent on maximal and minimal available flow rates. The total methanol flow rate (TF MeOH , Eq. 36) was 278.4kmol/h. The total DME flow rate (TF MeOH , Eq. 60) was 14.6kmol/h. The total by-product production of hydrogen was 576kmol/h, which was not included in the objective function.

Conclusion
The re-usage of waste raw materials can have positive effects on the amount of resources, waste and pollutants generated within industries. Selecting sustainable raw materials including renewable resources, reuse of waste, bio-based, and municipal solid wastes plays an important economic and environmental role.
The applied linear technique is a simple method for selecting between different raw materials for different product production by using basic easy non-mathematical or mathematical Nonlinear Programming (NLP) and Mixed Integer Nonlinear (MINLP) algorithms. The primary benefit of this technique is that it allows the selection of sustainable raw materials for optimal production conditions of different products by using the Aspen Plus simulator.
The applied linear technique measures product production from basic components by using a linear dependency between them. The slope of lines presents the conversion of product production from basic components of different raw materials.
Modifying existing methanol processes allows for 5.76MEUR/a higher additional profit by finding improved ratio factors of raw materials: f NG :f BG :f WW :f MSW = 0.1:0.1:0.3:0.5. The total methanol flow rate was 293kmol/h. Modifying existing methanol and DME production processes allows for 5.94MEUR/a higher additional profit by finding improved ratio factors of raw materials: f NG :f BG :f WW :f MSW = 0.1:0.1:0.3:0.5, which was the same as in methanolonly production. The total methanol and DME were 278.4kmol/h and 14.6kmol/h. The most promising raw material was municipal solid waste, which provides a higher perspective factor. Different raw materials for methanol production can easily be selected without mathematical algorithms by using the perspective factor.
The selection solution obtained was close to the optimum.