Integration of low-grade heat from exhaust gases into energy system of the enterprise

The paper presents a Process Integration application for waste heat utilisation from exhaust gas streams with partial condensation. It is based on the hot composite curve construction representing the gaseous mixture cooling with accounting for the condensable vapour part's gas–liquid equilibrium. With cold composite curve for streams requiring heating, the Pinch Point is determined. On this basis, the heat exchanger network (HEN) structure for utilised heat integration into the factory's energy system is developed. It accounts for the possible splitting of two-phase flow on gas and liquid streams and plate heat exchanger (PHE) type selection for specific positions in HEN. The method is illustrated by a case study of heat utilisation from exhaust gases after superheated steam tobacco drying and flue gases from natural gas-fired boiler. Heat transfer areas of PHEs in HEN are optimised with the total annualised cost as an objective function. The received solution's payback period is less than four months, with a substantial saving of energy, up to 10.9 TJ/y. It also leads to the reduction of CO2 emissions up to 600 t/y. About 3830 t/y of steam is not discharged to the atmosphere and as the water returned to the production process. To manuscript “Integration of Low-Grade Heat from Exhaust Gases into Energy System of the Enterprise”


Introduction
A growing need for energy characterises the sustainable development of humankind. However, even with the widening use of renewable sources, the primary way of energy generation is to combust fossil fuels with the emission of CO 2 and other harmful substances polluting the environment. A considerable part of this energy is wasted in the industry with outgoing streams, cooling utilities, and losses to the environment. According to the analysis presented in a paper by Papapetrou et al. (2018), the potential of waste heat available in the EU only is up to 300 TWh/y, with 33% of low-grade heat at temperatures below 200 °C, and 25% with temperatures 200-500 °C. Most of this waste heat is available in industrial zones (Huang et al. 2017). The use of this wasted energy can limit demand for fossil fuel combustion, leading to the conservation of resources, reduction of carbon dioxide emissions, and lower pollution of the environment. There is a potential of global emissions reduction by 44% in 2035, with most share achieved with waste heat usage that results in savings of primary energy (Oluleye et al. 2016).
A considerable part of the waste heat is going to the atmosphere with different off-and flue gases in many industrial sectors. The temperature of exhaust gases and their composition is determined by the conditions in the process of their origin. In many cases, the exhaust gas or some of the exhaust gaseous mixture components can condense to the liquid state being cooled down to specific temperatures (Varbanov et al. 2005). In this process, along with the sensible heat of gas cooling, the phase transition's latent heat is released. The relative share of sensible and latent heat is determined by exhaust gas composition and the cooling process's final temperature. In the majority of practical applications, the condensable part of the gaseous exhaust mixture is water vapour. Its latent heat is about 500 fold higher than heat capacity, and the heat of condensation can be a substantial part of total heat balance even at its small content in the mixture with not condensing gases. The typical examples of such exhausts are flue gases after different fuels combustion in furnaces, ovens, stoves, boilers. When the fuel contains sulphur, the condensing water with sulphur oxide in the gas can form sulphuric acid, promoting the heat exchanger's corrosion. It is recommended cooling gas to temperatures not lower than steam condensing temperature to limit this effect, e.g. 90 °C (Jin et al. 2019). However, in this case, a considerable amount of latent heat and water would be lost, and SOx discharged into the atmosphere elevating its pollution. To avoid this and to recuperate latent heat with flue gas cleaning from harmful oxides and generate some water, the direct contact economisers were proposed in a paper by Zhelev and Semkov (2004).
However, the advantages of recuperative heat exchangers make their use economically feasible even with heat transfer surfaces made from expensive materials. It is shown in the paper of Terhan and Comakli (2016) for condensing shelland-tube flue gas heat exchanger made of AISI316 quality stainless steel. The compact heat exchangers for this purpose are even more promising. They are smaller in volume and require much less material for heat transfer surface, as discussed in the book by Klemeš et al. (2015). The use of corrosion-resistant material allowed the use of latent heat in the heat pump's evaporator for heating water of the District Heating system (Vannoni et al. 2021). In all cases of flue gas condenser applications, heat exchanger design must be made for condensation in the presence of non-condensable gas (Li et al. 2019). The potential of waste heat utilisation from flue gases depends on the steam content in the exhaust gas. It is determined by the fuel type and method of its combustion. Different publications' data can vary from 5.5% on volume for a coal-fired power plant in Poland (Więcław-Solny et al. 2014) to 30% for the industrial waste incinerator (Aouini et al. 2014). The content of sulphur, nitrogen, and carbon oxides is also different and can require specific material for the condenser's heat transfer surface. Designing engineer must decide to use the waste heat recovery method in specific conditions on detailed technical and economic analysis of different available options.
Besides flue gases at energy generation, there is much heat wasted with exhaust gases in chemical, petrochemical, food, transport, communal and other sectors. In all these applications, the exhaust gas's vapour content can vary significantly with changing the share of sensible and latent heat for recovery. The drying technology where the latent heat in exhaust gases is predominant over sensible heat is superheated steam drying (Li et al. 2016). It is frequently used for drying different materials: food, wood, paper, coal, and sludge. One example of heat utilisation after superheated steam drying is described in the paper by Arsenyeva et al. (2016).
The efficient utilisation of heat from exhaust gases requires finding the best way to integrate it into the existing energy system. The Process Integration (PI) (Klemeš 2013) is an efficient tool for this purpose. It has been successfully extended to the number of implementations as, e.g. propertybased resources conservation networks (Saw et al. 2011), bioenergy supply chain (Foo et al. 2013), for hybrid power (electricity) systems (Wan Alwi et al. 2012), and integration of energy, water, and environmental systems (Baleta et al. 2019). It has shown the usefulness of the process integration methodology for finding the best solutions in heat recovery. However, it still needs an extension for accounting for this process's features in surface condensers. The Process Integration solutions can be improved using compact heat exchangers with intensified heat transfer . One of the efficient types of such exchangers is a plate heat exchanger (PHE). Due to considerable heat transfer enhancement in complex geometry channels, PHE has a much higher overall heat transfer coefficient than traditional shell and tube heat exchangers. It requires much less metal for the production of the heat transfer surface and allows obtaining economically viable solutions with its fabrication from costly corrosion-resistant materials, such as different stainless steels and other alloys. These features allow the use of PHEs in applications of process integration in severe conditions of the chemical and other industries . PHEs have low fouling tendencies (Hesselgreaves et al. 2017). In recent years, the efforts are made to improve the accuracy of PHE design in applications for condensing duties: as surface condensers of pure vapour (Tao and Ferreira 2019) and of vapour from its mixture with noncondensing gas (Kapustenko et al. 2020). It allows efficient use of PHEs in Heat Exchanger Networks (HENs) involving condensing processes. The structure of such HEN, and the design of PHEs as its components, can be optimised with Process Integration (PI). However, this methodology requires the novel modification accounting for the main features of PHE operation in processes of condensing vapour from its mixture with non-condensing gas.
This paper implements the process integration method (Klemeš et al. 2018) to find an efficient solution to utilise waste sensible and latent heat from exhaust gases using recuperative heat exchangers. It accounts for the nonlinear character of temperature effect on enthalpy and heat capacity flow rate in gaseous mixture streams with partial condensation of one of its components. The novel method is illustrated with a case study where utilisation of heat from boiler flue gases and heat of gas exhausting from the superheated steam drying process is considered. The utilisation of heat is performed using PHEs of specific types appropriate to each position of their application in HEN.

Methodology
The gaseous mixture's stream at a specific temperature contains its components' heat, including sensible heat and latent heat of these components phase transition to a liquid state. With the cooling down of the gaseous mixture to lower temperature, the heat contained in the stream diminishes. If there is no phase change of the components, only sensible heat is reduced in almost linear temperature dependence. The proportionality coefficient is equal to the gaseous mixture's sensible heat capacity that usually has small temperature dependence. On composite curves in PI, it is depicted by inclined segments of straight lines. In case of phase change of pure saturated vapour at constant pressure, its stream's internal heat not depends on temperature. It is depicted as horizontal segments of straight lines on Composite Curves. However, when the gaseous mixture stream contains a vapour component with a saturation temperature equal to the stream's temperature, the latent heat in it is not directly proportional to temperature. This change is following to equilibrium between condensing vapour and condensed liquid. The relation is not linear, and a segment of the curve depicts the process on hot composite curve. This feature of condensing gaseous streams must be accounted for in pinch analysis, as it can influence pinch position and minimal temperature difference there.
The heat released with gaseous mixture stream cooling in heat exchangers must be transferred to cold streams that require heating. For estimation of all heat that can be taken from hot streams at different temperatures in process integration, the hot composite curve can be used. This curve for exhaust gases must account for all forms of heat generated in the process of cooling: sensible heats of cooling vapour and non-condensing gas; the heat of already condensed liquid; latent heat of the vapour condensed in considered temperature interval. The decrease of enthalpy in the gaseous mixture stream during its cooling with a small temperature drop ΔT is determined as follows: , where G g , G v and G cn are mass flowrates of non-condensing gas, vapour and liquid condensate, kg/s; ΔT mx and ΔT cn are the temperature changes of gaseous mixture and condensate, K; c p-g , c p-v and c p-cn are specific heat capacities of noncondensing gas, vapour and condensate, J/(kg K); r v is the latent heat of vapour condensation, J/kg.
With the use of Eq. (1), the hot composite curve can be build assuming that: (i) for stream temperatures high than the saturation temperature of its vapour component, no phase transition happens, and only sensible heat has to be accounted; (ii) after the gaseous mixture stream is cooled down to saturation temperature of its vapour component it is keeping to be saturated at all lower temperatures; (iii) the overcooling of condensate is not considered, and Eq.
The overcooling of condensate is accounted for on the heat exchanger design stage, as it depends on heat exchanger construction features and flow structure.
The vapour in the gaseous mixture has its volumetric fraction ε v and partial pressure P v , according to which the saturation temperature is determined by function Tsat(P v ) expressing equilibrium conditions in K (the saturation temperature in centigrade is t s = T s −273.15 °C): (1) The vapour volume fraction is directly linked to its mass fraction and mass flowrates of the vapour and non-condensing part of the mixture. The non-condensing gases in the mixture can be regarded as ideal gases, and for them, the Equation of State for ideal gas has the following form: here, V Σ is the volumetric flow rate of the gaseous mixture, m 3 /s; P g is the total partial pressure of non-condensing gases in the mixture, Pa; R g is a specific gas constant of non-condensing gases as their mixture, J/(kg K), determined as follows: where R = 8314.5 J/(kmol K) is the universal gas constant; μ i is the molar mass of the individual gas or non-condensing gases mixture, kg/kmol.
The vapour at saturation is considered a real gas with real gas Equation of State Eq. (6). It is expressed in the same form as Eq. (4) with the introduction of compressibility factor z v and specific gas constant R v as follows : From Eq. (6) divided on Eq. (4) follows: For calculation of the compressibility factor z v the real gas Equation of State proposed by Peng and Robinson (1976) is used: where Here, v v is vapour molar volume, m 3 /kmol; T C is vapour critical temperature, K; P C is its critical pressure, Pa; ω is an acentric factor, for water vapour ω = 0.344.
The incoming gaseous mixture's saturation temperature is calculated by iterating with a first approximation of compressibility factor z v = 1. The partial vapour pressure P v is determined from Eq. (7), and at this value, the saturation temperature T s obtained from the equilibrium condition of (3) Eq. (3). At these T s and P v values, a new iteration for compressibility factor z v is calculated by Eq. (8). And so on until the difference of two successively calculated values of the compressibility factor is not bigger than the specified accuracy (0.0001), and the iterations are terminated. It usually requires no more than three iterating calculations. On constructing the hot composite curve, the all-temperature range of exhaust gas cooling development is divided into small equal intervals. The calculations are starting from the highest temperature by calculating stream enthalpy change at all successive temperature intervals. When the temperature of the gaseous mixture on certain interval j become smaller than inlet saturation temperature, the saturation conditions are assumed. The partial pressure of vapour P vj in this gaseous mixture is determined from the saturation condition at the temperature of interval end T mxj . It is expressed by function Psat v (T), describing vapour-liquid equilibrium: The mass flowrate of vapour at temperatures T mxi is determined from Eq. (7) at a fixed mass flowrate of non-condensing part of gaseous mixture: On these obtained values, the enthalpy change on each temperature interval is calculated by Eq. (1), and Hot Composite Curve is finally built. After this, the set of cold streams is determined, which need to be heated in that temperatures range. The Cold Composite Curve is constructed following the conventional PI rules (Klemeš 2013). By the Composite Curves, the Pinch position is determined, and the structure of HEN built following PI methods. It must also be accounting for the possibility of exhaust gas stream splitting on gas and liquid parts. It can be made after some point, where heat contained in a liquid phase is becoming bigger than heat contained in a remaining gaseous mixture.
It is illustrated in the Case Study presented in the following section. (10)

Case study
The case of a tobacco factory equipped with the plant for superheated steam drying of tobacco is considered. The drying plant parameters and possible heat utilisation streams are presented in a paper by Arsenyeva et al. (2016). A more detailed analysis of the factory's energy system revealed that a significant amount of heat is also wasted with flue gases leaving Natural Gas (NG) fired boiler. The boiler produces steam for drying plant and space heating of factory workshop, administrative, and other buildings. The heat for space heating is supplied through a heat exchanger by steam heating ethylene glycol solution circulating in a closed circuit. The temperature of exhaust flue gases of the boiler is 180 °C. In Table 1 are presented time-averaged parameters of exhaust gas streams leaving drying plant and boiler flue gases. There are also parameters of cold streams that require heating. It is ethylene glycol of the space heating circuit and feeds water for the boiler. After NG combustion, the volumetric flue gas composition is taken as 14% CO 2 , 11.5% H 2 O, 2.8% O 2 , and 72% N 2 . The exhaust gas after drying is a mixture of air and steam. The physical properties are taken according to Perry's Chemical Engineers' Handbook (Perry and Green 2008). The steam saturation pressure at temperature T is determined by Eq. (12).
The curve of enthalpy change in cooling flue gas after NG combustion is presented in Fig. 1. After the NG combustion depicted by curve 1, the flue gas can release 187.7 kW of heat on cooling to 0 °C. Of this heat, 73.9 kW is released as sensible heat before cooling to dew point at 49.5 °C, and mostly latent heat of condensing steam is 113.8 kW or about 1.5 times higher. The calculations are made for a steam share in flue gas 11.5% on volume. For comparison by curve 2 in Fig. 1 is presented the process of cooling the same amount of flue gas with steam volumetric content 23.0%, which can be at the combustion of biomass (Molcan et al. 2011). In this case, the sensible heat released before reaching the dew point at 64.8 °C is 69.9 kW, but latent heat over 3.3 times higher in value of 233.8 kW and is available at higher temperatures. It shows the importance of accounting for the type of fuel and steam content in flue gas when deciding about heat utilisation. Another source of waste heat is exhaust gas after the drying process (stream 2 in Table 1), with a steam content of 93.6% on volume. The enthalpy change on this gas cooling is shown by curve 3 in Fig. 1. The total change of enthalpy on cooling from 140 to 0 °C is 695.9 kW. The sensible heat of cooling to dew point temperature 108.8 °C is 17.7 kW or only 2.5% of the total. The principal amount of heat that can be received from these exhaust gases is generated by the predominantly latent heat of vapour condensation at temperatures below the dew point. With condensation of vapour, the temperature of exhaust gas changes according to equilibrium conditions, decreasing the heat transfer process's driving force in heat exchangers and the minimal temperature approach in PI. In the case considered, the total amount of heat that can be utilised from exhaust gases after drying is over three times bigger than heat from the flue gas after NG combustion in the boiler. It is also having much higher levels of temperature that is making its utilisation more convenient. The hot composite curve (HCC) is built to account for the heat generated by both waste heat sources, as shown in Fig. 2. It is obtained by summing the enthalpies in streams of flue gases of boiler fired with NG and exhaust gases from drying plant at the same temperatures. The total amount of heat obtained with the cooling of these exhaust gases to 0 °C is 884.0 kW. Figure 2 also presented the Cold Composite Curve (CCC) calculated for cold streams 3 and 4 of Table 1. The total amount of heat required to heat all cold streams is 736.5 kW. However, some part of the heat from hot streams is available at temperatures lower than cold streams require it. It can be seen from Fig. 2 where CCC is moved left to ΔTmin = 1 °C. The Pinch Temperature for cold streams is 50 °C. The amount of heat available from hot streams being cooled to 51 °C is 710.1 kW. Cold streams require at these temperatures 700 kW. Nevertheless, the utility boiler's additional heat may be needed for calculations at any ΔTmin and periods when the drying unit is not in operation. The use of a heat pump is not considered in this paper.
According to the "golden rule" for the development of optimal heat exchanger network (HEN) (Linnhoff et al. 1982), no heat has to be transferred across the Pinch. Below the pinch, is required to heat cold stream 4 (Table 1) with 36.5 kW. The available heat from hot streams is much bigger, 168 kW. It must be decided from what hot stream 36.5 kW of heat can be taken below the Hot streams Pinch temperature, using a heat exchanger with minimal cost. Both hot streams have enough enthalpy to fulfil this task (see Fig. 1).
With condensation of vapour, the flowrates of individual phases are considerably changing with temperature, as shown in Fig. 3 for exhaust gases after the drying process with volumetric steam content 93.6%. The heat capacity flow rate of exhaust gas streams is also significantly changing with temperature and heat capacity flowrates of phases in two-phase condensing flow (see Fig. 4).
At a temperature below 70 °C, more than 98% of steam is condensed, and the liquid's heat capacity flow rate becomes predominant. The cooling of the liquid phase at 60 °C can give about 60 kW of heat that is certainly enough to heat cold streams below pinch. The presence of gas in liquid can significantly increase the pressure drop in a heat exchanger. The two-phase stream of exhaust gas can be split on the liquid part directed to the liquid-liquid heat exchanger, and the gas part treated separately. In the case considered, it is discharged to ambient. After treatment, the obtained liquid can be directed back to the boiler or used for another factory's need to contribute to the water consumption economy.
The water content in the boiler's flue gases is 11.5% on volume and mass share of created condensate stream much smaller, as also its heat capacity flow rate, as shown in Fig. 5. It is no reason to split this stream. There are no cold streams that remain to utilise this heat below pinch, and it should be discharged to the atmosphere.
With Composite Curves in Fig. 2 and accounting that the exhaust gas cooling process has discussed features, HEN  Grid Diagram's structure is obtained (Fig. 6). It is made following the traditional version presented by Smith (2005).
However, there has also been some more recent development of an Extended Grid Diagram (Yong et al. 2015) and Shifted Retrofit Thermodynamic grid Diagram (Wang et al. 2020), which offer several even more enhanced features. This structure does not change with the variation of ΔTmin that can be optimised with an economic objective function. The optimal ΔTmin is also determining the Hot Pinch temperature. At this temperature, the stream 2 is split on gas and condensed liquid flows.
For heat recuperation at different HEN matches, specific types of PHEs are selected. It is made accounting for the nature of heat exchanging streams and their working temperatures. For cooling of exhaust gases from the drying plant, the plate-and-frame PHE TS6M produced by AlfaLaval (Alfa Laval 2020) is used. These PHE plates have corrugations with a somewhat elevated height of about 4 mm, comparing other PHE plates with a height of 2-3 mm. It allows having an increased cross-section area of channels to decrease pressure drop of heat exchanging stream that is important for gaseous streams and condensing duty applications. The calculations of steam-air condensation in this PHE were made using the mathematical model presented in a paper by Kapustenko et al. (2020) with heat and mass transfer coefficients determined according to Arsenyeva et al. (2014). The results are presented in Table 2 with the purchasing price in € estimated by Equation (Arsenyeva et al. 2016): For liquid-liquid duty on a position HE2 AlfaLaval plateand-frame PHE of type M3 is selected with plates having corrugation height 2 mm, which is efficient for liquid heat transfer at small channel length. The calculations are made according to the method described in the paper by Arsenyeva et al. (2009). The results of heat transfer area calculations are also presented in Table 2, with the price estimated according to Equation from paper (Arsenyeva et al. 2016).
Stream 1 of flue gases has an initial temperature of 180 °C. It is out of the working range for rubber gaskets of plate-and-frame PHE. Here, the heat exchange between gaseous and liquid streams must be performed. For cooling (13) Pp HE1 = 978 ⋅ Fa HE1 + 3100 of flue gases at position HE3 the welded pillow-plate heat exchanger (PPHE) is chosen to account for high temperature and demand to accommodate big gas flowrates that are directed in a channel between pillow panels (Arsenyeva et al. 2019). Table 2 presented the results of calculations of the PPHE heat transfer area obtained according to the method described in the paper of Arsenyeva et al. (2019). The price is estimated according to Equation for welded PHEs from the book by Klemeš et al. (2015): The cost of equipment installation IC = 41,170 € and cost of project development PC = 6060 € are taken based on data for real expenses on implementation at the factory the pilot substation for heat utilisation from exhaust gases of drying plant (Arsenyeva et al. 2016). The purchasing cost of all heat exchange equipment: Total capital investment cost: The annualised capital investment cost is determined according to Eq. (18), proposed in the book by Smith (2005): where ir is the yearly interest rate for capital borrowing and n is time in years for the borrowing of the capital (it is assumed ir = 0.10 and n = 3).
The price of steam is taken as 380 € kW −1. y −1 and on it operational cost OC is determined. It is assuming that the installed equipment is operating only during the heating season or half a year. Total annual cost: The influence of ΔTmin on total annual cost, annualised capital investment, and operational cost are shown in Fig. 7. Here, a minimum of TAC is observed at ΔTmin equal to 23 °C. In this case, the amount of 692.7 kW of heat is saved and would not need to be produced by the boiler for space heating. The cost of this saved energy in the form of steam in the half-year period of the heating season is 132,000 €. Capital investment for this ΔTmin option is 71,070 € or about 1.85 times lower, and payback period for the proposed waste heat utilisation system is about 3.2 months after the installation is commissioned.
The proposed system for heat utilisation from exhaust gases in 182 d of operation during the heating season saves about 10.9 TJ/y of heat produced by natural gas combustion. According to an analysis presented by Juhrich (2016), the carbon dioxide emission factor for such NG is about 55.16 t/TJ. Implementation of the proposed system is leading to a reduction of about 600 t/y of CO 2 emissions, as also accompanying SOx and NOx emissions produced with NG burning. The flowrate of condensed water from exhaust gases after drying plant at ΔTmin equal to 23 °C is 0.245 kg/s. It means that 3850 t/y of water is not emitted into the environment and, after some treatment, can be returned to a steam-generating boiler. It is leading to saving of that amount of freshwater.

Conclusions
The exhaust gases discharged into the environment after various industrial processes contain a considerable amount of energy (in sensible and latent forms) wasted if not properly utilised. The efficient utilisation of this heat and its integration into the enterprise's existing energy system is possible with the application of the Process Integration methodology and compact PHEs with enhanced heat transfer. The accurate estimation of heat available for utilisation from exhaust gases at different temperature levels requires the construction of a Hot Composite Curve accounting for the sensible and latent heat that can be extracted in the process of exhaust gas streams cooling. Composite Curve construction for exhaust gases with different content of the condensable vapour part is proposed. It accounts for the nonlinear character of stream enthalpy relation to temperature in cooling processes involving phase change of condensable component. The use of Process Integration allows identifying the optimum targeted structure of HEN accounting for streams requiring heating in the enterprise's energy system. The determined HEN's efficient realisation requires considering the correct choice of heat exchanger type for each position depending on the stream's nature and process parameters. It is preferably compact PHEs with accounting for the possibility of condensing streams splitting at some temperature on gas and liquid phases for more efficient heat exchange in individual heat exchangers. The final selection of PHEs on different HEN positions is made with economy optimisation on Total Annual Cost as an optimising criterion. The software tools for the novel method implementation has been developed. The method is illustrated with the presented Case Study considering the utilisation of heat from two exhaust gas streams exiting at one enterprise. There is the stream of exhaust gas after the process of superheated steam tobacco drying with steam content 93.6% on volume and stream of flue gas after natural gas-fired boiler with volumetric steam content 11.5%. It shows PI application capabilities for utilising waste heat from exhaust gases using efficient PHEs selected according to their position in heat utilisation HEN. The implementation of developed HEN allows saving about 10.9 TJ/y of heat energy. It means the reduction of NG consumption and corresponding CO 2 emissions on 600 t/y. About 3830 t of steam is not discharged to the ambient, and as water can be returned to the production process.
Funding No funding was received to assist with the preparation of this manuscript.

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Conflict of interest
The authors have no conflicts of interest to declare that are relevant to the content of this article.