The Thermal Economy of a Circulating Medium and Low Temperature Waste Heat Recovery System of Industrial Flue Gas

Energy is the material basis for human survival and the driving force for the development of national economy [1-4]. After the two industrial revolutions, the economy of human society began to develop at an accelerating speed, and the energy utilization modes are upgrading continuously. As a result, now all countries around the globe are facing two prominent problems: energy shortage and environmental pollution [5-9]. Due to the limited technological level and the historical problems of traditional industrial development mode, China's industrial production and manufacturing processes generally have problems such as high resource consumption and large energy waste. Therefore, China's industrial field has great energy-saving potential [10-14]. How to fully recover and utilize industrial waste heat on the premise of causing no disturbance to the original industrial production and manufacturing process has become a research focus for field scholars in the world [15, 16].

Waste heat recovery is an effective way to recycle energy. Loni et al. [17] summarized and discussed the research on waste heat recovery using Organic Rankine Cycle (ORC), and launched an investigation of the heat-electricity cogeneration system based on ORC. In view of the problem that the absorption heat pump and compression heat pump in traditional waste heat recovery systems cannot consider the temperature rise and efficiency, An et al. [18] proposed to use the thermally-coupled hybrid compression/absorption heat pump to achieve high-efficiency and high-temperature output; moreover, in order to fit in different scenarios, they also built a large temperature-rise cycle and a high-temperature output cycle, and constructed a mathematical model in ASPEN PLUS to predict the performance of the cycles. Based on the pinch analysis of a given heat exchange network, Wang et al. [19] proposed a systematic approach to integrate the heat pump into the industrial process, and analyzed the influence of waste heat temperature and temperature rise on the selection of heat pump; the proposed heat pump integration method can be further extended to other low-grade industrial waste heat recovery processes. Fito et al. [20] elaborated on how the selection of indicators changes the design of waste heat recovery system in district heating; then for three possible waste heat temperatures, they optimized the design, and the different optimizations were instructed by two energy indicators and the overall efficiency; after that, they evaluated the annual performance of the system using Sankey and Grassman diagrams, and gave a comparison of the optimized designs. Peris et al. [21] proposed to optimize the thermal economy of waste heat recovery systems based on experimental applications, they developed, calibrated, and verified a comprehensive facility model constructed based on actual operation data, this model could be applied to optimize the thermal economy, reveal the influence of the geometric parameters of organic fluid, circulation structure and main components, and formulate control strategies for obtaining the optimal cost-effective solution.

The waste heat recovered by traditional industrial waste heat recovery systems is mostly high-temperature flue gas and combustible gas. There’re quite a few problems with these systems such as low waste heat utilization rate, poor comprehensive utilization, and incomplete waste heat utilization equipment and system, also, the waste heat of medium and low temperature flue gas that accounts for more than 50% of the total waste heat resources has been ignored by these systems. Under the condition that the heat amount of the industrial waste heat recovery system is given, building a circulating system to pursue higher thermal efficiency is more reasonable, however, few studies have concerned about the changes in the economy of such circulating industrial waste heat recovery system. Therefore, to fill in this research gap, this paper attempts to study the economy of a circulating medium and low temperature waste heat recovery system (hereinafter referred to as “the circulating system” or “the proposed system”). The second chapter gives a thermodynamic analysis of different medium and low temperature waste heat recovery modes of industrial flue gas; the third chapter analyzes the economy of the circulating system; and the fourth chapter uses experimental results to verify the effectiveness and accuracy of the thermodynamic and thermo-economic models constructed in this paper.

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Figure 2. Flow of the trans-critical ORC system

The ORC system takes low boiling-point organics as working medium, its four core components are: waste heat boiler, turbine, working medium pump, and condenser; and its supporting system includes separator and regenerator. ORC system has simple structure and good economic performance. The research object of this paper is the 100℃~300℃ low-temperature flue gas discharged from industrial boilers, and using ORC system to recover the waste heat of this part of flue gas could achieve a good recovery effect. In this paper, a trans-critical ORC system with two-stage compression and two-stage expansion was constructed, and the flow of the system is given in Figure 2.

In the proposed system, at first the working medium absorbs heat from the main heat source and enters the high-pressure turbine for expansion work, then it is heated by the heat exchanger of the regenerated heat source, and enters low-pressure turbine for expansion work. The low-temperature working medium output from the high-pressure compressor is heated by the high-temperature working medium output from the low-pressure turbine through the regenerator, then, it enters the intermediate heat exchanger to release heat to the secondary circulating heat exchange working medium; after that, it is cooled by the condenser and compressed by the low-temperature compressor, and finally, it enters the heat exchanger of the main heat source through intermediate cooling and regeneration. This paper mainly analyzes the thermodynamics and thermal economy of the secondary circulating heat exchange process.

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Figure 3. Structure of the secondary ORC system

Figure 3 shows the structure of the secondary ORC system. In the figure, ψ_hi and ψ_hp respectively represent the inlet temperature and outlet temperature of flue gas; ψ_ei and ψ_ep respectively represent the inlet temperature and outlet temperature of cooling water; ψ_ho represents the corresponding flue gas temperature at the pinch point of temperature difference of evaporator and condenser, and ψ_qo represents the corresponding cooling water temperature at this point; Δψ_w and Δψ_d respectively represent the pinch point temperature difference of evaporator and condenser. Figure 4 shows the temperature-entropy diagram of the secondary ORC system.

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Figure 4. Temperature-entropy diagram of the secondary ORC system

According to the temperature of the medium and low temperature main heat source of industrial flue gas, this paper chose several organic working media such as candidate working media of the ORC system, including cyclohexane, n-ethane, pentane, and isopentane, etc. Table 2 lists the basic thermodynamic properties and environmental protection attributes of the candidate working media.

In the ORC system, the heat transfer process at the evaporator has two stages: preheating stage and evaporation stage. Assuming q_h represents the mass flow of flue gas, q_g represents the mass flow of working medium, ρ_oh represents the flue gas’s average specific heat capacity at constant pressure, ψ_h,n=(ψ_hi+ψ_hp)/2 represents the qualitative temperature, then, based on the law of energy conservation, there are:

${{E}_{w,pre}}={{q}_{h}}{{\rho }_{oh}}\left( {{\psi }_{ho}}-{{\psi }_{hp}} \right)={{q}_{g}}\left( {{f}_{5}}-{{f}_{2}} \right)$              (16)

${{E}_{w,eva}}={{q}_{h}}{{\rho }_{oh}}\left( {{\psi }_{hi}}-{{\psi }_{ho}} \right)={{q}_{g}}\left( {{f}_{3}}-{{f}_{5}} \right)$          (17)

$\Delta {{\psi }_{w}}={{\psi }_{ho}}-{{\psi }_{w}}$        (18)

Combining Formula 16, 17, and 18:

${{\psi }_{w}}=\frac{{{f}_{5}}-{{f}_{2}}}{{{f}_{3}}-{{f}_{2}}}{{\psi }_{hi}}+\frac{{{f}_{3}}-{{f}_{5}}}{{{f}_{3}}-{{f}_{2}}}{{\psi }_{ho}}-\Delta {{\psi }_{w}}$            (19)

Based on above formula, under the condition of a given set of (ψ_hi, ψ_hp, Δψ_w), the corresponding ψ_w can be obtained through iterations, further, the physical parameters of state points 3 and 5 in the cycle can be determined. Formula 20 gives the calculation formula of heat exchange in evaporator:

${{W}_{d}}={{q}_{g}}\left( {{f}_{3}}-{{f}_{2}} \right)={{q}_{h}}{{\rho }_{oh}}\left( {{\psi }_{hi}}-{{\psi }_{ho}} \right)$          (20)

The heat exchange area of the evaporator can be calculated by Formula 21:

${{S}_{d}}=\frac{{{E}_{d}}}{{{V}_{d}}\Delta {{\psi }_{d}}}$        (21)

Assuming: V_w represents the total heat transfer coefficient of the evaporator; f_h represents the convective heat transfer system on the flue gas side, to simplify calculation, the V_w can be approximately equivalent to f_h; NUN represents the Nusselt number; REN represents the Reynolds number; PRN represents the Prandtl number, then for the flue gas side, there is:

$NU{{N}_{h}}=0.27REN_{h}^{0.63}PRN_{h}^{0.36}$       (22)

Assuming: μ_h represents thermal conductivity of flue gas, R_w represents the outer diameter of evaporator pipe, then, Formula 23 gives the calculation formula of convective heat transfer coefficient of the flue gas side:

${{f}_{h}}=\frac{NU{{N}_{h}}\times {{\mu }_{h}}}{{{R}_{w}}}$          (23)

The heat exchange in the condenser can be calculated by Formula 24:

${{E}_{d}}={{q}_{g}}\left( {{f}_{4}}-{{f}_{1}} \right)={{q}_{e}}{{\rho }_{oe}}\left( {{\psi }_{ep}}-{{\psi }_{ei}} \right)$          (24)

Formula 25 gives the calculation formula of the heat exchange area of condenser:

${{S}_{d}}=\frac{{{E}_{d}}}{{{V}_{d}}\Delta {{\psi }_{d}}}$          (25)

Assuming: R_d represents the outer diameter of the condenser pipe, E_di represents the inner diameter of the condenser pipe, f_e represents the heat transfer coefficient of water in the condenser pipe, f_g represents the heat transfer coefficient of working medium outside the condenser pipe, then, the total heat transfer coefficient of the condenser can be calculated by Formula 26:

$\frac{1}{{{V}_{d}}}=\frac{{{R}_{d}}}{{{R}_{di}}{{f}_{e}}}+\frac{1}{{{f}_{g}}}$        (26)

As for the condenser, there is:

$NU{{N}_{e}}=0.023REN_{h}^{0.8}PRN_{h}^{0.4}$        (27)

Then, f_e can be calculated by Formula 28:

${{f}_{e}}=\frac{M{{g}_{e}}\times {{\mu }_{e}}}{{{R}_{di}}}$      (28)

Assuming: μ₁ represents the thermal conductivity of the liquid, φ₁ represents the liquid density, φ_h represents the steam density, λ₁ represents the dynamic viscosity of the liquid, ψ_d represents the average condensation temperature, ψ_y represents the pipe wall temperature, then, f_g can be calculated by Formula 29:

${{f}_{g}}=0.725{{\left[ \frac{\beta h\mu _{1}^{3}{{\phi }_{1}}\left( {{\phi }_{1}}-{{\phi }_{h}} \right)}{{{\lambda }_{1}}{{R}_{d}}\left( {{\psi }_{d}}-{{\psi }_{y}} \right)} \right]}^{0.25}}$           (29)

Assuming: Δψ_max and Δψ_min respectively represent the maximum and minimum terminal temperature differences during the heat exchange process of heat exchanger, then Formula 30 gives the calculation formula of the logarithmic average temperature difference of evaporator and condenser:

$\Delta {{\psi }_{m}}=\frac{\Delta {{\psi }_{max}}-\Delta {{\psi }_{min}}}{ln\frac{\Delta {{\psi }_{max}}}{\Delta {{\psi }_{min}}}}$          (30)

The output work of the turbine can be calculated by Formula 31:

$D{{E}_{u}}={{q}_{g}}\left( {{f}_{3}}-{{f}_{4}} \right)$         (31)

The isentropic efficiency of the turbine can be calculated by Formula 32:

${{\delta }_{u}}=\frac{{{f}_{3}}-{{f}_{4}}}{{{f}_{3}}-{{f}_{4r}}}$        (32)

The power consumption of the working medium pump can be calculated by Formula 33:

$H{{E}_{QB}}={{q}_{g}}\left( {{f}_{2}}-{{f}_{1}} \right)$       (33)

The isentropic efficiency of the working medium pump can be calculated by Formula 34:

${{\delta }_{QB}}=\frac{{{f}_{2r}}-{{f}_{1}}}{{{f}_{2}}-{{f}_{1}}}$        (34)

The total investment cost of the ORC system includes four parts: evaporator, condenser, turbine, and working medium pump. If the system is equipped with additional equipment such as regenerator and separator, then the total investment cost is the sum of the input in the 6 parts, and Formula 35 gives the calculation formula of system investment cost:

$\lg {{D}_{IN}}={{\gamma }_{1}}+{{\gamma }_{2}}lg\omega +{{\gamma }_{3}}{{\left( lg\omega  \right)}^{2}}$         (35)

Assuming: D_IN represents the basic investment cost based on carbon steel structure and environmental pressure, ω represents the basic parameters of the cost of each component of the system, S represents the heat exchange area of corresponding heat exchanger, HE_QB represents the consumed work of the pump, DE₁ represents the output work of the turbine, U_rw represents the capacity of the separator.

This paper adopted the standup-type gravity gas-liquid separator in the research, its capacity U_rw can be calculated by the following steps. Assuming: φ_i and φ_h respectively represent the density of liquid and the density of gas corresponding to state points 4 and 2, ω_r represents a constant coefficient, then, the gas flow rate in the gas-liquid separator can be calculated by Formula 36:

${{v}_{w}}=\frac{3}{4}\times {{\gamma }_{r}}\sqrt{\frac{{{\phi }_{1}}-{{\phi }_{h}}}{{{\phi }_{h}}}}$         (36)

Assuming: U_MAX-h represents the maximum volume of the gas flow, q₂ represents the mass flow of working medium at the turbine inlet, then, there is:

${{U}_{MAX\text{-}h}}=4800\times \frac{{{q}_{2}}}{{{\phi }_{h}}}$         (37)

Formula 38 gives the calculation formula of the cylinder diameter of the separator:

$Z{{J}_{rw}}=0.02\sqrt{\frac{{{U}_{h\text{ }max}}}{{{v}_{w}}}}$           (38)

Assuming γ_CS represents the pressure correction coefficient, and the pressure borne by components such as evaporator, regenerator and separator is uniformly represented by CS, then, based on above formula and the separator specification, the nominal volume of the separator can be further calculated:

$lg{{\gamma }_{CS}}={{D}_{1}}+{{D}_{2}}\lg CS+{{D}_{3}}{{\left( \lg CS \right)}^{2}}$          (39)

Assuming γ_CL and γ_SY respectively represent the material correction coefficient and the comprehensive correction coefficient, through correction, the system investment cost D_SY can be updated as follows:

${{D}_{SY}}={{D}_{CS}}{{\gamma }_{SY}}={{D}_{CS}}\left( {{\alpha }_{1}}+{{\alpha }_{2}}{{\gamma }_{CL}}{{\gamma }_{CS}} \right)$            (40)

This paper mainly analyzes the performance of the ORC system from the perspective of thermal economy. In this paper, the heat exchange area required for unit net output power HEA, the turbine size FS, and the levelized electric energy cost FIP were selected as evaluation indicators of the economic performance of the circulating system; and the net output power DE_CL and the exergy efficiency δ_wa were selected as evaluation indicators of the thermodynamic performance of the circulating system. Assuming δ_uh represents the electric efficiency, then, Formula 41 gives the calculation formula of the system’s net output work DE_CL:

$D{{E}_{CL}}={{\delta }_{uh}}D{{E}_{u}}-D{{E}_{o}}$        (41)

The exergy efficiency δ_wa of the circulating system can be calculated by Formula 42:

${{\delta }_{wa}}=\frac{D{{E}_{CL}}}{T{{R}_{in}}-T{{R}_{out}}}$         (42)

HEA can be calculated by Formula 43:

$HEA=\frac{{{S}_{w}}+{{S}_{f}}+{{S}_{d}}}{D{{E}_{CL}}}$        (43)

Assuming RF_u represents the volume flow of the fluid of working medium at turbine outlet, f_IN and f_OUT respectively represent the enthalpy at the turbine inlet and outlet, then, FS can be calculated by Formula 44:

$FS=\frac{\sqrt{R{{F}_{u}}}}{{{\left( {{f}_{IN}}-{{f}_{OUT}} \right)}^{0.25}}}$        (44)

According to above formula, the smaller the value of FS, the lower the investment cost of the system, and the better the economic performance of the system. Assuming SYW represents the system operation and maintenance cost, D_OY represents the total annual system investment, then Formula 45 gives the calculation formula of the total investment of the circulating system D_total:

${{D}_{tot}}=D{{O}_{Y}}IRD+SYW$       (45)

Assuming ξ represents the bank interest rate, ε represents the normal operation life, then Formula 46 gives the calculation formula of the investment recovery factor IRD:

$IRD=\frac{\xi {{\left( 1+\xi  \right)}^{\varepsilon }}}{{{\left( 1+\xi  \right)}^{\varepsilon }}-1}$         (46)