Diagrams of Entropy for Ammonia–Water Mixtures: Applications to Absorption Refrigeration Systems

international journal of refrigeration 82 (2017) 335–347

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Diagrams of entropy for ammonia–water mixtures: Applications to absorption refrigeration systems

Diovana Aparecida dos Santos Napoleao a,*, Jose Luz Silveira b, Giorgio Eugenio Oscare Giacaglia c, Wendell de Queiroz Lamas a,b, Fernando Henrique Mayworm Araujo b a Department of Basic and Environmental Sciences, School of Engineering at Lorena, University of Sao Paulo, Lorena, SP, Brazil b Institute of Bioenergy Research, IPBEN-UNESP, Associated Laboratory of Guaratingueta, Sao Paulo State University, Guaratingueta, SP, Brazil c Post-graduate Programme in Mechanical Engineering, Department of Mechanical Engineering, University of Taubate, Taubate, SP, Brazil

ARTICLE INFO ABSTRACT

Article history: The objective of this work is to calculate the entropy of ammonia–water mixture as a func- Received 31 October 2016 tion of temperature, pressure, concentration, and other thermodynamic properties associated Received in revised form 1 June to absorption process, to support energy and exergy analysis of absorption refrigeration 2017 systems. This calculation is possible because a novel mathematical modelling was devel- Accepted 26 June 2017 oped for this attempt. This determination will allow simulation and optimisation of absorption Available online 30 June 2017 refrigeration systems, giving major importance in determining the values of thermodynamic properties of ammonia–water mixtures, such as enthalpy and entropy. A mathematical Keywords: modelling for thermodynamics properties calculation at liquid and vapour phases of ammonia– Absorption refrigeration system water system is developed. The studies were based on the enthalpy vs. concentration diagram (ARS) obtaining the enthalpy in the liquid phase corresponding at a temperature range from 80 − Ammonia–water mixtures °C to 40 °C. The mixtures enthalpy values were calculated for ammonia (h1c) and water Entropy diagrams (h2c) by using a non-linear regression program. The evaluation of thermodynamic proper- Thermodynamic properties ties in this work was discretised by formulating appropriate equations for each type of substance. However, thermodynamic properties of mixtures can be determined based on data from simple substances and mixing laws, or from an equation of state that considers the mixture concentration. The consistency of experimental data indicates the most suitable method to be used in entropy calculation. © 2017 Elsevier Ltd and IIR. All rights reserved.

Diagrammes entropiques pour des mélanges ammoniac-eau : applications aux systèmes frigoriﬁques à absorption

Mots clés : Système frigoriﬁque à absorption ; (ARS) ; Mélanges ammoniac-eau ; Diagrammes entropiques ; Propriétés thermodynamiques

* Corresponding author. Department of Basic and Environmental Sciences, School of Engineering at Lorena, University of Sao Paulo, Estrada Municipal do Campinho, s/n, 12602-810, Lorena, SP, Brazil. E-mail address: [email protected] (D.A.d.S. Napoleao). http://dx.doi.org/10.1016/j.ijrefrig.2017.06.030 0140-7007/© 2017 Elsevier Ltd and IIR. All rights reserved. 336 international journal of refrigeration 82 (2017) 335–347

Nomenclature l Liquid phase o Ideal gas state α=β=A = B Constants of mixture compounds = C = D = a = b Subscript Λij =Λji Adjustable binary interaction parameters 0 Values of reference in vapour phase of Wilson’s equation 1c Value calculated for ammonia Cp Specific heat capacity [kJ/kg.K] 2c Value calculated for water F Objective function A Absorber G Gibbs free energy [kJ/kg] C Critical value MCALC. Predicted values G Generator MEXP. Property experimental value MIXT. Mixture P Pressure [MPa] MIXT.IDEAL Ideal mixture R Universal constant of ideal gas [kJ/kmol.K] MIXT.ACTUAL Actual mixture T Temperature [K] i Related to ammonia V Volume [m3] j Related to water h Specific enthalpy [kJ/kg] o Ideal gas state s Specific entropy [kJ/kg.K] r Reduced thermodynamic properties x Ammonia concentration [kgammonia/kgmixture]

Superscript E excess g Vapour phase

The absorption machines have the advantage of using 1. Introduction thermal energy instead of electricity, which today has become more expensive, especially in the context of the lack of in- Advances in absorption technology have motivated the devel- vestments in the national power supply. opment of this work. A frustrating aspect of this study is the The absorption facilities also allow recovering the heat lost lack of fundamentally systematic and detailed analysis of ab- in case of turbines and other types of facilities, which operate sorption technology, which is often omitted in the scientific based on co-generation. Along with these advantages, the ab- literature. sorption machines are characterised by their simplicity, since In Alefeld and Radermacher (1994), related positive aspects there are no internal moving parts (pumps placed apart), which of this issue have been addressed, adducing its inter-disciplinary guarantees a silent and vibration-free operation. nature, and showing the need of works combining different In the absorption system, employing water and ammonia scientific areas, such as physics, chemical engineering, and me- is one of the most reported in the literature, considering the chanical engineering. data of enthalpy tables and diagrams according to concentra- Contributions from different fields give us a better under- tion; however the entropy has not been given the same standing of absorption technology, such as the following: physics attention, due to the absence of corresponding data of this ther- comprising a wide spectrum; chemical engineering including modynamic property, hitherto available in the literature, making chemical corrosion and physical-chemistry; and mechanical a broader and more detailed study on the thermodynamics of engineering considering heat and mass transfer, fluid dynam- this system necessary, in order to determine the exact inter- ics, materials science, and applied thermodynamics. relationship of entropy correlated with other properties. However, in recent years, the development of absorption Configurations, main thermodynamic and hydraulic pa- technology presented variations; in particular, the industry in- rameters, and some design guidelines and operating experiences creased activities with manufactured products, resulting in this of a medium-temperature, ammonia–water-based compression/ sector’s improvement through research and development, with re-absorption heat recovery system for district domestic hot a lot of interest shown in this matter, which is actually con- water production were presented by Minea and Chiriac (2006). firmed by scientific publications in absorption refrigeration The critical point of the ammonia–water mixture was calcu- system (ARS) area monitoring. lated directly from the Helmholtz free energy formulation by In Seyfouri and Ameri (2012), several configurations of in- Akasaka (2009), in order to obtain simple correlations for the tegrated refrigeration system consisting of a compression chiller critical temperature, pressure, and molar volume for a given and an absorption chiller powered by a micro-turbine to gen- composition. A parametric analysis of a combined power/ erate cooling at low temperatures were analysed. cooling cycle, which combines the Rankine and absorption The absorption technology, mainly in air conditioning refrigeration cycles, uses ammonia–water mixture as the systems, is adopted with preferential use of a binary solution working fluid and produces power and cooling simultane- consisting of water and lithium bromide (imported solution). ously, was presented by Vasquez Padilla et al. (2010). However, the most common cooling system uses ammonia as A set of five equations describing vapour–liquid equilib- refrigerant and water as absorbent. This solution is manufac- rium properties of the ammonia–water system was presented tured and used in Brazil. by Patek and Klomfar (1995). Four of different correlations for international journal of refrigeration 82 (2017) 335–347 337

the thermodynamic properties of ammonia–water mixtures large quantities by certain liquids or saline solutions. The used in studies of ammonia–water mixture cycles described refrigerant can be separated from the solution resulting from in the literature were compared by Thorin et al. (1998). A theo- the absorption by heating. Thus, the absorption cycle re- retically based crossover model, which incorporates a crossover places the compressor with the generator-absorber assembly from singular thermodynamic behaviour at the critical point and pump, while the evaporator, condenser, and the expan- to regular thermodynamic behaviour far apart from the criti- sion valve operate in the same way as in the compression cal point, was presented by Edison and Sengers (1999) for the cycle. thermodynamic properties of ammonia. A new method for ther- In a continuous operating system (Fig. 1), the ammonia modynamic properties computations at high temperatures and vapour (2) is separated from ammonia–water solution (1) by pressures using Gibbs free energy and empirical equations for heating the solution in the generator; the ammonia vapour is bubble and dew point temperature to calculate phase equi- condensed in a condenser, and the liquid ammonia (4) is ex- librium was presented by Xu and Yogi Goswami (1999). panded in an expansion valve. However, in the evaporator (5) Modelling of the thermodynamic properties of ammonia– the ammonia is evaporated by exchanging heat necessary for water refrigerant mixture was developed by Mejbri and Bellagi its evaporation and performing the “refrigerating effect”. The (2006). ammonia, in the vapour state (6), is absorbed by the ammonia The objective of this work is to calculate the entropy of poor solution (10). The absorption reaction is exothermic and ammonia–water mixture as a function of temperature, pres- occurs in a vessel known as absorber, producing a solution rich sure, concentration, and other thermodynamic properties in ammonia (ammonia–water, NH4OH). The rich solution (7) is associated to absorption process, to support energy and exergy then pumped by the liquid pump (8), through a heat ex- analysis of absorption refrigeration systems. This calculation changer and into the generator (1), ending the cycle. The poor is possible because a novel mathematical modelling was de- solution exiting the generator (3) passes through a heat ex- veloped for this attempt. This determination will allow changer, pre-heating the rich solution, passes through an simulation and optimisation of absorption refrigeration systems, expansion valve (entered at point 9) to equalise the pressure giving major importance in determining the values of ther- with the ammonia vapour coming from the evaporator (6) and modynamic properties of ammonia–water mixtures, such as enters the absorber (10). enthalpy and entropy.

2. Fundamentals of absorption refrigeration 3. Mathematical modelling system In this section, a novel mathematical modelling to calculate The basic principle of a refrigeration system is to transfer heat the entropy of ammonia–water mixture as a function of tem- from a low temperature reservoir to a high temperature res- perature, pressure, concentration, and other thermodynamic ervoir that can be the environment (Silva, 1994). properties associated to absorption process, to support energy The absorption diagram shown in Fig. 1 is based on the and exergy analysis of absorption refrigeration systems at liquid fact that the vapours of some refrigerants can be absorbed in and vapour phases is presented.

Fig. 1 – Basic ARS diagram (Zukowski, 1999). 338 international journal of refrigeration 82 (2017) 335–347

3.1. Liquid phase used in the simulation to calculate the activity coefﬁcient of a component in the liquid phase are: Wilson, NRTL, UNIQUAC, 3.1.1. Excess enthalpy calculation method UNIFAC, Margules, Van Laar, and regular solution. The excess enthalpy at certain pressure and temperature can The program ChemCAD III was used in this work to deter- be expressed by Eqs. (1) and (2). mine the parameters Λ12 and Λ21 of Wilson equation through the model used for the calculation of parameters. Initially the E hh=−MIXT.. ACTUAL h MIXT IDEAL (1) program set temperature (K), pressure (atm), and molar frac- tion (mol) for the respective units. These features were chosen =+ for ammonia–water mixture, which was selected into soft- hxhxhMIXT. IDEAL ii jj (2) ware menu, even as the Wilson model, and then the linear To obtain enthalpy values in liquid phase of ammonia– regression is started. After these software conﬁgurations all water mixture the enthalpy-concentration diagram was used desired parameters values were obtained. (Costa, 1976) in case of graphical representation of enthal- pies of solutions of different concentrations at constant 3.1.3. Actual entropy calculation method temperature for different pressures. A corresponding tempera- The objective of the development of this work is to deter- ture range between −40 °C and 80 °C was used for development mine the actual entropy of ammonia–water mixture. The actual of these calculations. entropy and excess entropy of mixture are presented by Eqs. (6) and (7).

3.1.2. Excess entropy calculation method =+− + + E sxsxsRxxxxsMIST. ACTUAL ii jj() iln i j ln j (6) Excess entropy is obtained by Eqs. (3) and (4) using excess enthalpy values and excess Gibbs free energy. hGEE− sE = (7) E T ss=−MIXT.. ACTUAL s MIXT IDEAL (3)

Wilson’s equation, which is based on molecular consider- sxsxsRxxxx=+−()ln + ln MIXT. IDEAL ii jj i i j j (4) ations, was used for determination of excess Gibbs free energy of a binary solution, Eq. (8) (Prausnitz et al., 1999). The entropy values for components of ammonia–water mixture were obtained from reference tables (Reynolds, 1979) E G =− +ΛΛ−+ xxiiijjjjjiiln() xxx ln() x (8) in the temperatures range corresponding to absorption refrig- RT eration cycle considered in this work. Values obtained were subjected to a linear regression method using the REGRE soft- According to Prausnitz et al. (1999), the excess Gibbs energy ware (Caceres-Munizaga et al., 1994), and later to compute si is deﬁned with reference to an ideal solution in the sense of and sj corresponding to entropy of ammonia and water in liquid Raoult’s law and Henry’s law, also directly related to Wilson phase of an ideal mixture. Determination of entropy evalua- (1964). tion of actual mixture was obtained by sum of excess entropy Binary Wilson’s equation parameters, Λij and Λji, were de- with entropy of ideal mixture. termined by Eqs. (9)–(11). The analysis of non-linear regression is an optimisation problem, in which a certain objective function should be VT() α Λ = j RT minimised; the objective function is somewhat arbitrary, but ij e (9) VTi () must include experimental data of the proposed model. The

REGRE program is based on the modiﬁed Marquardt method, β VT() Λ = i RT which is an appropriate combination of local linearisation ji e (10) VT() method and the steepest descent method. The objective func- j tion described in the program is: A V = (11) n 2 ⎛ ⎞ − T 7 FMM=−∑() ⎝⎜1 ⎠⎟ EXP.. CALC (5) B Tc i=1 i

Wilson’s equation can be used in here because the liquid Absolute errors between property experimental values (MEXP.) phase of this system presents a completely miscible mixture and values predicted by the model on study (MCALC.)were Prausnitz et al., 1999; Wilson, 1964). minimised. This calculation is based in subroutines of ChemCAD ( Values of α and β in Eqs. (9) and (10) were calculated by using III program. the Λ and Λ factors determined by software ChemCAD III, The program ChemCAD III (Chemstations, 1998) is a high 12 21 level steady state process simulator and applicable to several from the data of ammonia–water mixture at temperatures from (12) and (13). industrial processes. It is similar to other commercial simu- 0 to 80 °C, and represented as Eqs. lators, including a series of thermodynamic options for the most α=aaT + different applications where the simulator is designed. ij (12) The equations of state commonly used are Soave–Redlich– β= + Kwong, Peng–Robinson, and Lee–Kesler; and among models bbTij (13) international journal of refrigeration 82 (2017) 335–347 339

In software ChemCAD III these parameters (Λ12 and Λ21)are referred to as A12 and A21.

4. Results and discussion

4.1. Results obtained for liquid phase

The studies were based on the enthalpy vs. concentration diagram obtaining the enthalpy in the liquid phase corresponding at a temperature range from 80 °C (353.15 K) through −40 °C (235.15 K). The mixtures enthalpy values calculated for ammonia (h1c) and water (h2c) corresponding to the polynomial Eqs. (14) and (15) were obtained by using a non-linear regression program (REGRE) (Caceres-Munizaga et al., 1994).

2 hTT1c =−1,. 015 41 + 6 . 24861 ⋅ − 0 . 009416381 ⋅ +⋅0. 00001569906 T3 (14)

2 hTT2c =−994.. 168 + 2 776773 ⋅ + 0 . 004352178 ⋅ −⋅0. 000004393749 T3 (15) Fig. 2 – Diagram of entropy vs. concentration of ammonia From Eqs. (14) and (15) calculated enthalpy values, the en- (liquid phase of the mixture). thalpy of ideal mixture (ammonia–water) was obtained. The excess enthalpy was obtained by the difference between actual and ideal calculated mixture enthalpy. For the results of properties in excess (enthalpy, entropy and The excess Gibbs energy was calculated using the Wilson Gibbs free energy), a diagram to elucidate the behaviour of the model [Eq. (9)] for the binary components. The Wilson equa- ammonia-water mixture in the liquid phase, corresponding to tion parameters were determined using the computer program a pressure of 0.1 MPa (1 atm) and temperature of 323 K (50 °C) ChemCAD III. was plotted. The excess entropy was obtained by the computed difference between the excess enthalpy and excess Gibbs energy with 4.2. Vapour phase respect to temperature. Values of calculated entropies for ammonia (s1c) and water (s2c) mixtures were adjusted using the 4.2.1. Equation of state for pure component polynomial Eqs. (16) and (17). The fundamental Gibbs free energy equation (G) of a pure component may be obtained from known relationships for volume =− + ⋅ − ⋅ 2 sTT1c 6.. 71612 0 04869194 0 . 000095628 and heat capacity as a function of temperature and pressure. +⋅0. 0000000910479 T3 (16) According to Ibrahim and Klein (1993), the fundamental equation for Gibbs free energy can be expressed in integral form

2 as Eq. (18): sTT2c =−6.. 400273 + 0 33386 ⋅ − 0 . 00004291395 ⋅ +⋅0.T 00000002359528 T3 (17) T P T ⎛ ⎞ =− + + − Cp Gh00 Ts∫∫ CdTVdPTp ∫⎜ ⎟ dT (18) ⎝ T ⎠ The actual entropy was calculated by the sum of the excess T00P T 0 entropy and ideal entropy, shown in Eq. (6). The entropy vs. concentration thermodynamic diagram of where h0,s0,T0, and P0 correspond to specific enthalpy, spe- ammonia in the liquid phase shows the pressure curves cor- cific entropy, temperature, and pressure of reference in the responding to 0.1 MPa and 2 MPa and temperature curves vapour phase. The reduced volume (Vr) and specific heat ca- corresponding to a range of 0 °C (273.15 K) to 190 °C (463.15 K) pacity (CP) are correlated according to Eqs. (19) and (20). (Fig. 2). 2 For constructing this thermodynamic diagram, real values g =++++RTr C2 C3 CP4 r Vr C1 3 11 11 (19) of mixture property were considered. A spreadsheet of ther- PrrrT T Tr modynamic properties of excess, ideal and actual using the go, 2 software MS-Excel©, was developed. The equations allow to Cp=+ D12 D Trr + D 3 T (20) obtain data on the properties from different values of concentration of ammonia present in the mixture (0.05, 0.2, 0.4, For vapour phase in mixtures system, the empirical rela- 0.6, 0.8, 1.0 kg of ammonia kg−1 of mixture). tionship corresponding to Gibbs free energy can be expressed These values were used because the mixture presents great by substituting Eqs. (19) and (20) into Eq. (18). After integra- variation, which does not permit to work with a continuous tions, intensive function of Gibbs free energy for pure ammonia function. and water in the vapour phase is related to Eq. (21). 340 international journal of refrigeration 82 (2017) 335–347

2 2 3 3 g =−g g + − +DT2 rr − DT20,, + DT3 rr − DT3 0 Table 1 – Coefﬁcients of pure components of the Gr hr,,00 Tsr r DT110rr DT, 2233 ammonia–water mixture (Ziegler and Trepp, 1984). 3 2 −−−+2 −+DT3 rrr DTT30, DT102rr()ln T ln T r,, DT r DTT20 rr Coefﬁcient Ammonia Water 22 − × −2 × −2 + ()− +−()+−Pr 43CP20r,, +CP20rr T C1 1.049377 10 2.136131 10 Tr llnPPCPPCrr ln ,,01 rr 02 +1 3 3 4 C2 −8.288224 −3.169291 × 10 Tr Tr Tr,0 − × +2 − × +4 CP 12CP 11CP T CP3 12CCP3 11CP3 T C3 6.647257 10 4.634611 10 +−3 r 30r, +30rr, +4 r −40r, + 40rr, − × +3 11 11 12 11 11 12 C4 3.045352 10 0.0000 Tr Tr,0 Tr,0 3Tr 3Tr,0 3Tr,0 D1 3.673647 4.019170 (21) −2 −2 D2 9.989629 × 10 −5.175550 × 10 −2 −2 D3 3.617622 × 10 1.951939 × 10 L Eq. (22) is obtained by Eq. (21) differentiating with respect hr,0 4.878573 21.821141 g to the reduced temperature (Tr). hr,0 26.468873 60.965058 L sr,0 1.644773 5.733498 g g s 8.339026 13.453430 ⎛ G ⎞ r,0 ∂⎜ r ⎟ ⎝ ⎠ 22− 32− Tr,0 3.2252 5.0705 Tr =−g −−2 +2 +DT220rrr + DT, T +2DDT330rrr+ DT, T hTr,0 rrr DTT10, Pr,0 2.000 3.000 ∂Tr 22 33 ⎛ ⎞ − 1 −− +D3 22− −()− −2 D123ln ⎝⎜ ⎠⎟ DDTrrrTT,0 CP1 rrrPT,0 r Tr 2 −2 −−−12CP30r, Tr 2 3 5 5 13 RTBr T D2 2 RT Br T D3 ⎛ 1 ⎞ −+41612CPT2 rr CP20 r, T r − CPT3 rr + 2 2 11 hr =+ −RTBr T D1 ln ⎜ ⎟ − RTBr T D2 Tr,0 ⎝ ⎠ 2 3 Tr − 32 3 −−−3 3 11 313− 4CP40rr, T − RTBr T D32−+41612 RTCPTBrr RTCP Brr20, T − RTCPT Brr3 −+4CPT4 rr 11 − Tr,0 3 11 − 4RTBr C4 P Tr (30) (22) To calculate the reduced entropy in the vapour phase, In Eq. (21), the superscript g corresponds to the vapour phase ⎡∂G ⎤ the term r based on Eq. (21) was used, which provides in the ideal gas state. The reduced thermodynamic proper- ⎢ ∂ ⎥ ⎣ Tr ⎦P ties are expressed with the subscript r, being presented by Eqs. Eq. (31). (23)–(27). ⎛ 1 ⎞ sRsRDRDTRDTRD=−−g −2 +ln ⎜ ⎟ +−2RD T RD T = T r r,0 12rr 3 1220⎝ ⎠ rr, Tr (23) Tr TB 2 2 ⎛ ⎞ + 3RRD3 Trr−− RD30 T , P r+ −2 R ln ⎝⎜ ⎠⎟ 3RC2 Prr T 22 Pr,0 P = − 3RC20 Pr, − 11RC30 Pr, Pr (24) − 12RC P T 4 −+11RC P T 12 − P 20rr, 4 3 rr 12 B Tr,0 Tr,0 31− 2 3 + 11RC4 Prr T − 11RC40 Pr, 12 (31) = G 3 3Tr,0 Gr (25) RTB

4.2.2. The entropy equation of mixtures in vapour phase = h hr (26) The ammonia–water mixture in the vapour phase is assumed RTB to have an ideal solution behaviour. The entropy of mixture in the vapour phase is represented by Eq. (32) (Xu and Yogi s Goswami, 1999). sr = (27) R

g g g sxsxss=+−ga (1 gw) + MIXT. (32) The reference values of the reduced properties are MIXT. −1 −1 R = 8.314 kJ kmol K ,TB = 100 K, and PB = 0.1 MPa. =− {}()+−()()− In terms of reduced variables, Eqs. (26) and (27) can be sRxLnxxLnxMIXT. 11 (33) written as Eqs. (28) and (29). The coefficients values for Eqs. (21) and (31) are presented ⎡ ∂ ⎛ G ⎞ ⎤ in Table 1. hRTT=− 2 ⎜ r ⎟ Br⎢∂ ⎝ ⎠ ⎥ (28) ⎣ Tr Tr ⎦P 4.2.3. Results obtained for vapour phase ⎡∂G ⎤ The fundamental Gibbs free energy equation was used to sR=− r ⎢ ∂ ⎥ (29) develop the mathematical model relevant for calculation of ther- ⎣ Tr ⎦P modynamic properties of the vapour phase, such as specific ⎡ ∂ ⎛ G ⎞ ⎤ enthalpy, specific entropy, and specific entropy of mixing in- By inserting the term ⎜ r ⎟ obtained in Eq. (22) in Eq. ⎢∂ ⎝ ⎠ ⎥ ⎣ Tr Tr ⎦P volved in the cooling system by water–ammonia absorption. (28), the reduced enthalpy calculated in the vapour phase as- The Gibbs free energy equation, given for the pure compo- sociated with the ammonia–water system was determined by nent, may be derived from known values of volume and heat Eq. (30). capacity as a function of temperature and pressure relation- international journal of refrigeration 82 (2017) 335–347 341

Fig. 3 – Entropy vs. ammonia concentration diagram for pressure ranges from 0.2 to 0.4 MPa.

ships. In order to determine the mixture entropy in the vapour The equations developed provided data on the properties phase, reduced thermodynamic properties presented in de- for different values of ammonia concentration in the mixture scription of this section was used, as well as specific coefficients (0.1, 0.2, 0.4, 0.6, 0.8 kg of ammonia kg−1 of mixture), consid- for pure components, resulting in the development of these ering a temperature range from 20 °C (293.15 K) through 200 calculations. °C (473.15 K) and pressure from 0.1 through 2.0 MPa, shown in For the calculations associated with vapour phase, ther- Figs. 3–7 that present two graphical compounds for each one, modynamic properties of ammonia–water mixture were related which are a comparison between two specific cases, such as to the equation of state proposed by Ziegler and Trepp (1984), in Fig. 3, presented concentration for 0.2 MPa and for 0.4 MPa, and subsequently, mathematical models were developed to de- and so on. termine the calculations of the pure components and the The entropy vs. ammonia concentration diagram allows for mixture belonging to vapour phase. the study of mixture of ammonia and water for an absorp- Entropy values of the mixture in the vapour phase were con- tion refrigeration system through simulation and optimisation sidered for plotting thermodynamic diagrams, also drawing at of value ranges presented. the same time a spreadsheet of thermodynamic properties Data obtained by means of the proposed mathematical using the software MS-Excel©. model underwent adjustments essential to plot these 342 international journal of refrigeration 82 (2017) 335–347

Fig. 4 – Entropy vs. ammonia concentration diagram for pressures of 0.6 MPa and 0.8 MPa.

diagrams in the vapour phase, due to the difﬁculty of Some data from this study, relating the pressure vs. ammonia standardising some parameters involved in this system. concentration, were compared with results presented by To compare this work with data reported by Rizvi and Rizvi and Heldemann (1987) who studied the ammonia– Heldemann (1987) it was necessary to adjust some points, thus water system for a wide range of temperatures corresponding assisting the preparation of diagrams pressure vs. concentra- to Figs. 8–10. tion of ammonia; however, there was a good accuracy of these A work associated with the study of isothermal data from data, contributing to the analysis of refrigeration systems. vapour–liquid equilibrium for ammonia–water system at tem- In current literature, pressure is often used in bar and temperatures ranging 306–618 K and pressures up to 22 MPa was perature in Kelvin, so that it makes no sense to use developed in Rizvi and Heldemann (1987). Figs. 8–10 compare concentration values higher than those used in this literature. isothermal data from Rizvi and Heldemann (1987) with results It should be emphasised that the temperature range chosen of this work near the critical temperature of ammonia. to develop this work is from −40 °C (233 K) through 80 °C (353 K), In the study of the vapour–liquid equilibrium, the ammonia– a rather restricted range as compared to data reported in the water system becomes complex to obtain the exact amount literature, where ranges of pressure and temperature vary related to the composition of the vapour phase. The uncer- widely for the determination of thermodynamic properties as- tainty of the composition of this water in vapour phase becomes sociated with the cooling system by water–ammonia absorption. a difﬁcult problem to solve for studies associated with the international journal of refrigeration 82 (2017) 335–347 343

Fig. 5 – Entropy vs. ammonia concentration diagram for pressure ranges from 1.0 to 1.2 MPa.

vapour–liquid equilibrium, and some data available in the lit- pressure, and temperature. This sort of diagram permits exergy erature on this subject are referred to as inconsistent. analysis in absorption refrigeration system applying The data calculated in this work showed good correlation with mixtures of ammonia and water and it can be used to help the data of Rizvi and Heldemann (1987); however, they were ob- many scientists working on the exergetic optimisation of tained at a temperature about 2 °C below the critical temperature designs and analysis. In general, engineers use this type of of ammonia, being predicted that the results of the work of Rizvi studies. and Heldemann (1987) reported temperature values exceeding In the current Brazilian energy context and several devel- the results of this work, even though the general trend of the oping countries, the use of absorption thermal machines data as a function of concentration is similar. appears to be a promising option. Cooling systems represent the best alternative to produce cold in regions where there is little distribution of electrical power, because they are powered directly through the burning of biogas (or other fuel) as a heat 5. Conclusions source or use of residual heat of co-generation systems. In the energy landscape scenarios, the use of absorption technol- The present study shows the new three-dimensional ogy can be more interesting than compression refrigeration diagrams of entropy, as function of concentration of NH3, systems. 344 international journal of refrigeration 82 (2017) 335–347

Fig. 6 – Entropy vs. ammonia concentration diagram for pressure ranges from 1.4 to 1.6 MPa.

The evaluation of thermodynamic properties in this work equation suitable for binary systems was used, whereas was discretised by formulating appropriate equations for each the parameters belonging to this mathematical model were type of substance (ammonia–water). However, thermody- determined by the software ChemCAD III. Since used relation- namic properties of mixtures can be determined based on data ships between the properties of mixtures made by Reynolds from simple substances and mixing laws, or from an equa- (1979) were used, adjustment points for making some of tion of state that considers the mixture concentration. The the entropy vs. concentration diagram is justiﬁed, and due to consistency of the experimental data indicates the most suit- the mathematical model implemented, the curves originat- able method to be used in entropy calculation. Several equations ing in this diagram are not started from zero concentration of state are discussed in the literature; however, due to their point. development complexity, they are not used to determine the For the vapour phase of the mixture ammonia–water data thermodynamic properties of the mixture. adjustment, it was necessary to obtain the ordering of points During the development of this work, thermodynamic prop- between the working temperatures, making three-dimensional erties of liquid phase and vapour associated with ammonia– diagrams of entropy vs. concentration. In these three- water mixture of absorption refrigeration systems were studied. dimensional diagrams for the vapour phase, it was observed In the liquid phase of ammonia–water mixture the Wilson that with increasing pressure there occurred a decrease in international journal of refrigeration 82 (2017) 335–347 345

Fig. 7 – Entropy vs. ammonia concentration diagram for pressure ranges from 1.8 to 2.0 MPa.

entropy value associated with the cooling system by absorb- However, data of certain thermodynamic properties ing the mixture. show good accuracy and can contribute to the exergy The scientific literature presents discussion of the ammonia– and thermo-economic analysis of absorption refrigeration water system associated with the difficulty of determining the systems. concentration in the vapour phase, due to the uncertainty of the composition of water present at this stage, making the data available inconsistent. This paper presents some comparative data with other Acknowledgments studies; however, it is necessary to emphasise the difficulty of comparison, since the related scientific papers present a wide Dr. Jose Luz Silveira thanks his “Productivity Scholarship in range of pressure and temperature associated to ammonia– Research,” supported by the Brazilian National Council water mixture, making it impossible in most cases to compare for Scientific and Technological Development (CNPq) (303295/ other studies with this work that was developed for a narrow 2014-7). Dr. Giorgio Eugenio Oscare Giacaglia thanks his Visiting range of temperature and pressure with the application of ab- Professor Scholarship provided by the University of Taubate sorption refrigeration systems. (UNITAU Ordinance No. 448/2016). 346 international journal of refrigeration 82 (2017) 335–347

Fig. 8 – Phase diagram for the critical point of the ammonia corresponding to temperature of 306.5 K.

Fig. 9 – Phase diagram for the critical point of the ammonia corresponding to temperature of 341.8 K. international journal of refrigeration 82 (2017) 335–347 347

Fig. 10 – Phase diagram for the critical point of the ammonia corresponding to temperature of 355.7 K.

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