Design of 10 kW Low Temperature Power Cycle Using Amine— CO2 Fluid

Our thermodynamic study indicated that low temperature power cycle using amineCO2 fluid can obtain the performance equal to or higher than that of the current organic Rankine cycle. We designed a 10 kW test equipment. We set high temperature heat source is hot water at the temperature of 90°C and the flow rate of 8,200kg/h, which is a coolant from a gas engine. The heat and mass balance of the equipment was calculated thermodynamically. The result showed the power of 10.5kW and the system efficiency of 7.3 per cent at the the amine – CO2 fluid flow rate of 1,000kg/h, and the turbine expansion ratio of 4.8. The preliminary estimation shows as follows. The diameter and rotational speed of the turbine blade are 0.115m and 54,400min-1, respectively. The number, width, and length of the recuperator plates are 20, 117mm, and 835mm, respectively. The height and cross sectional area of the absorption bed are 0.35m and 0.027m2, respectively.


Introduction
Low temperature heat below 200℃ is produced massively (Shindo et al., 2008). Kalina cycle using NH3 and organic Rankine cycle using HFC-245fa (CHF2CH2CF3) can generate electricity from the low temperature heat. However, the former is toxic and corrosive and the latter has a high GWP value, which is required to reduce by the Kigali amendment to the Montreal Protocol and the Regulation (EU) No. 517/2014. As a process that utilizes less toxic and low GWP working fluid, the present authors have proposed to use Amine-CO2 absorption/desorption system for power generation. The thermodynamic simulation shows the maximum power of the low temperature cycle using 30 mass% methyl diethanol amine (MDEA)-H2O solution (CO2/MDEA mole ratio: 0.15) is equal to that of the Organic Rankine cycle using HFC245fa. The experimental results suggest the low temperature cycle using the MDEA-based solution containing carbon dioxide is available as a low temperature cycle (Ogawa et al., 2019). This paper shows mass and heat balance, preliminary designs of a recuperator, a turbine, and an absorption bed in a 10 kW low temperature power cycle using MDEA-based solution. Figure 1 shows a low temperature cycle using amine-CO2 fluid. An amine-CO2-H2O solution(S8) is pressurized in a pump(P1) and heated in a recuperator(Hx3). The preheated fluid(S12) is heated at a boiler (Hx1) by hot water (S1), whose temperature and flow rate are 90℃ and 8,200 kg/h, respectively. A two phase flow (S2) from the boiler (Hx1) is separated into a H2O-CO2 gas mixture (S11) and a residue (S13) by a gas-liquid separator (Sep1). The H2O-CO2 gas mixture (S11) drives a turbine (Ex1) and expands adiabatically. The residue (S13) heats a pressurized amine-CO2-H2O solution (S3). The expanded H2O-CO2 gas mixture (S5) and the residue (S13) cooled in the recuperator (Hx3) are mixed in a mixer (M1) and cooled to 40℃ in an CO2 absorber/cooler (Hx2) where CO2 is absorbed in the residue and water mixture.

Mass and Heat Balance
It is assumed that the values of the polytropic efficiency of P1, the isentropic efficiency of EX1, the pressure losses of Hx1, Hx2, Hx3, and Sep1 are 75%, 80%, 0kPa, respectively. The pinch temperatures of Hx1, Hx2, and Hx3 are assumed to be 4℃, 5℃, and 5℃, respectively.     The vapor phase fraction at the EX1 outlet is more than 0.88 (Nishikawa, 1965). The pressure at the pump inlet is the minimum value when the vapor phase fraction is zero. The process simulator VMGSim TM v10.0 (Thermodynamic model: Amines) of the Virtual Materials Group Inc. simulated the model. Its power of 10.5 kW and efficiency of 7.3 per cent are achieved at the fluid flow rate of 1,000 kg/h and expansion ratio of 4.8. Table 1 shows the mass and heat balance.
Figures 2, 3, and 4 show the temperatures of the both side fluids as a function of the accumulated heat exchange in the recuperator (Hx3), the boiler (Hx1), and the cooler (Hx2), respectively.
In the boiler the low temperature fluid is the heated amine-CO2-H2O solution (S12), which desorbs the CO2 -H2O gas mixture. Its equilibrium temperature between liquid and gas phases increases with CO2 desorption and water vaporization.

Recuperator
The total heat load of a plate heat exchanger (PHE) is as follows: where Q is total heat load of a PHE (W), n is number of the plates for heat exchange, Qi is local heat load (W), Ui is local overall heat transfer coefficient (W/(m 2 ⋅K)), Ai is local heat transfer area (m 2 ), and Δ TLMTD,i is local logarithmic average temperature difference (℃). The local overall heat transfer coefficient Ui is calculated as follows : where αH,i and αL,i are local film heat transfer coefficients (W/(m 2 ⋅K)) for hot and cold streams, respectively, δ is plate thickness (m), λ is thermal conductivity (W/(m⋅K)) of the plate material. The local logarithmic average temperature difference ΔTLMTD,i is defined as follows : where ΔTA,i and ΔTB,i are local temperature differences at both ends of local area, respectively.
The local film heat transfer coefficients are calculated by empirical correlations: where Nui is local Nusselt number, Rei is local Reynolds number, Pri is local Pradtl number, μi and μw,i are local viscosity (Pa⋅s) at stream and at wall temperatures, respectively (Arsenyeva et al., 2010). Rei , Pri , and Nui are defined as follows : where ρi is local density (kg/m 3 ), vi is local velocity (m/s), deq,i is local hydraulic equivalent diameter (m), Cp,i is local specific heat at constant pressure (J/(kg⋅K)), and ki is local thermal conductivity (W/(m⋅K)). Equations (1)-(7) calculate the plate length as a function of the accumulated heat exchange in the recuperator, whose plate width, distance between plates, plate thickness, and number of plates are 117 mm, 2.35 mm, 0.5 mm, and 20 mm, respectively. The plate length results in 835 mm. The reference of thermophysical properties for working fluid (Amine-CO2-H2O) is the thermodynamic model: Amines of the Virtual Materials Group Inc. Figure 5 shows the plate length as a function of the accumulated heat exchange in the recuperator.  Figure 6 shows the temperatures of high and low temperature streams as a function of the plate length in the recuperator. The calculated exit temperature of the low temperature stream of 66℃ is nearly equal to that in the mass and heat balance of 64℃.

Turbine
The expansion ratio of the turbine is 4.8. We adopt a single stage radial flow turbine. The max efficiency of a radial flow turbine should reach at the specific speed of 0.6 and the rotor speed/thermal insulation speed ratio of 0.7 (Inoue et al., 2006). The specific speed, rotor speed, and thermal insulation speed are related in Eqs. (8)

Absorption Bed
The mass transfer rate of CO2 through the liquid layer on the absorption bed is expressed as follows: where NCO2 is mass transfer rate (mol/s) of CO2, KCO2 is mass transfer coefficient in the liquid film (mol/(m 2 ⋅s)) of CO2, a is gas-liquid contact area per unit volume (m 2 /m 3 ), xCO2 is mole fraction of CO2 in liquid phase, * is at equilibrium to the bulk gas, subscript av is arithmetic mean, S is cross sectional area (m 2 ) of absorption bed, Z is height (m) of absorption bed. The overall material balance of the absorption bed is expressed as follows : where L is unit cross section liquid flow rate (mol/(m 2 ⋅s)), and 1,2 are inlet and exit of the absorption bed, respectively.
A multiple regression equation approximating the ka is obtained using the experimental results as follows :

Plate Length (m)
High T Low T ka = c1 + c2 (V/S) + c3 LCO2,1 + c4T + c5 PCO2 (18) where T is temprature (℃), PCO2 is partial pressure (kPa) of CO2. Table 2 shows the coefficients of Eq. (18).  (19) Figure 7 shows the height, cross section area, and volume of the absorption bed as a function of liquid flow per specific area. The height of the absorption bed increases with the liquid flow per specfic area. The cross sectional area and volume of the absorption bed decreases with the liquid flow per specfic area. The height of the absorption bed becomes nearly constant after the liquid flow per specific area of 0.01m/s. Thus the design point results in the liquid flow per specific area of 0.01m/s. The absorption bed is the height of 0.35m and cross sectional area of 0.027m 2 .
The pressure drop of the absorption bed is expressed using the Ergun equation : where Δp is pressure drop of the absorption bed (Pa), Dp is spherical equivqlemt particle diameter (m), ε is bed porosity (Ergun, 1952 ;Akgiary and Saatci, 2001).
If the driving force of the liquid flow through the absorption bed is only gravity, the pressure drop of the absorption bed should be less than the static pressure at the bottom of column filled by liquid.
Equations 20 and 21 result in the maximum value of V/S of 0.335m/s, which is larger than the liquid flow per specific area of 0.01m/s at the design point. Therefore the liquid is expected to flow downwards by the gravity regardless of the pressure drop.

Conclusion
Thermodynamic simulation of the low temperature cycle using MDEA-based solution shows the power of 10.5 kw and efficiency of 7.3% at the fluid flow rate of 1,000 kg/h and expansion ratio of 4.8 using hot water whose temperature and flow rate are 90℃ and 8,200 kg/h, respectively.
The designed recuperator is a plate heat exchanger consisting twenty plates whose width and length are 117 mm and 835 mm, respectively.
The designed turbine is a single stage radial flow turbine whose blade diameter and number of rotations are 0.115 m and 5.44 × 10 4 min -1 , respecrively.
The designed absorption bed is the height of 0.35 m and cross sectional area of 0.027 m 2 at the liquid flow per specific area of 0.01 m/s. Cross sectional area Volume