Adiabatic Sorption of Ammonia-Water System and Depicting in p-t-x Diagram

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1 Adabatc Sorpton of Ammona-Water System and Depctng n p-t-x Dagram J. POSPISIL, Z. SKALA Faculty of Mechancal Engneerng Brno Unversty of Technology Techncka 2, Brno CZECH REPUBLIC Abstract: - Absorpton cycles desgners often utlze p-t-x dagrams of workng mxtures for frst suggeston of new absorpton cycles. The p-t-x dagrams enable fast correct determnaton of saturate states of lqud (and gaseous) mxtures of refrgerants and absorbents. The workng mxture sn t only at saturated state durng a real workng cycle. If we know pressure and temperature of an unsaturated mxture, exact poston determnaton s possble n the p-t-x dagrams too. But there are stll processes uneasy to draw n the p-t-x dagrams, namely adabatc sorpton. The adabatc sorpton s very nterestng phenomenon that occurs when vapor of refrgerant s n contact wth unsaturated lqud absorbent-refrgerant mxture and exchange of heat s forbd between the system and an envronment. Ths contrbuton ntroduces new auxlary lnes that enable correct poston determnaton of the adabatc sorpton process n the p-t-x dagram of ammona-water system. The presented auxlary lnes were obtaned from common functons for fast calculaton of water-ammona system propertes. Key-Words: - adabatc sorpton, auxlary lnes, p-t-x dagram, ammona-water system 1 Introducton Ths paper presents the new auxlary lnes for Absorpton cycles represent thermally drven cycles for wde varety of utlzng. Intensve development of the absorpton cycles has led to sgnfcant ncreasng of the coeffcent of performance (COP) n last 20 years. The most mportant way of COP ncreasng s based on reutlzng of senstve heat of workng mxtures. Another possble way for ncreasng of COP s based on reutlzaton of absorpton heat generated durng absorpton of refrgerant vapor n unsaturated mxture. The generator-absorber heat exchange (GAX) cycles utlze ths phenomenon. Heat generated durng an absorpton process s used for a desorpton process n a generator. The absorpton heat s mportant parameter of up to date absorpton cycles. Good utlzng of the absorpton heat can be reached only f absorpton cycle desgners have correct detal nformaton about an absorpton process. Absorpton cycle desgners often utlze p-t-x dagrams of workng mxtures for frst suggeston of new absorpton cycles. The p-t-x dagrams enable fast correct determnaton of saturate states of lqud (and gaseous) mxtures of refrgerants and absorbents. The p- t-x dagrams serve as basc nstrument for absorpton cycle desgnng. But these dagrams don t enable to obtan detal nformaton about adabatc sorpton process. mprovng of ths stuaton. The auxlary lnes base from common functons for fast calculaton of water-ammona system propertes. The new auxlary lnes enable correct poston determnaton of the adabatc sorpton process n the p-t-x dagram of an ammona-water system. 2 Mathematcal descrpton The adabatc sorpton s useful phenomenon that occurs durng contact of refrgerant vapor and an unsaturated lqud absorbent-refrgerant mxture. Exchange of heat s forbdden between the mxture and an envronment. The unsaturated mxture s absorbng the refrgerant vapor and the mxture temperature ncrease. Ths process contnues untl the saturated state s reached. Mathematc descrpton of ths process s based on conservaton of Saturated refrgerant vapor T v, h v, x v Unsaturated mxture T 1, h 1, x 1 p = constant ADIABATIC ABSORPTION Fg. 1 Inlets and outlets of the adabatc absorpton process Saturated mxture T 2, h 2, x 2

2 energy. That s realzed by utlzng of conservaton of enthalpy durng sobarc absorpton. The schema at fg. 1 shows consdered nlets and outlet of the process. Where T, h, x mean temperature, enthalpy and mole fracton of NH3. Subscrpts v, 1, 2 dentfy propertes of saturated refrgerant vapor, unsaturated mxture and saturated mxture. Mole fracton of NH3 n saturated refrgerant vapor s equal to 100%. Correspondng enthalpy and temperature s calculated from equatons obtaned from [1]. Saturated mxture parameters were calculated wth utlzng of the functons for fast calculaton of water-ammona system propertes [1] [2] [3]. Mole concentraton and temperature of unsaturated mxture s requred together wth absorpton pressure as nput parameters. The functons for fast calculaton of mxture propertes provde nformaton only for saturated state of the mxture. So, we must use an approprate approach for determnaton of unsaturated mxture specfc enthalpy. At ths paper we used knowledge of specfc thermal capacty of the saturated mxture and temperature of the saturated mxture. Unsaturated lqud mxture enthalpy h1 was calculated wth utlzng of equaton (1). T 1, p, x 1 h v = f (p) T 1 = f (p, x 1 ) c p1 = f (x 1, T) h 1 = f (T, x 1 ) h 1 = h 1 - c p1 ( T 1 -T 1 ) x = x 1 ; h = h 1 ; h = h 1 x = k (h -h)/ h v x = (x + x) / (1 + x) h = (h + x. h v ) / (1 + x) h = f (T, x) - h h < ε x 2 = x h 2 = h T 2 = f (p, x 2 ) Fg. 2 Iteratv calculaton of adabatc sorpton saturate state + h1 = h1 c p1 ( T1 T1 ) (1) Where superscrpt ' denotes saturated state of lqud mxture and subscrpt 1 denotes lqud mxture wth mole fracton of NH3 equal to mole fracton of the orgnal lqud unsaturated mxture. Pressure s assumed at constant level. Equatons for calculaton of the saturated mxture specfc thermal capacty, temperature of the saturated mxture and the saturated mxture specfc enthalpy are depended only on actual pressure and NH3 mass concentraton. T 1 = f (p, x 1 ) (2) h 1 = f (T 1 ', x 1 ) (3) c p1 = f (T 1 ', x 1 ) (4) After calculaton of the mentoned equatons, we compare value of enthalpy of the unsaturated lqud mxture and the saturated lqud mxture wth same mole fracton of NH3. If enthalpy of the unsaturated mxture s below enthalpy value of the saturated one, the absorpton of NH3 vapor contnues. Mass concentraton of NH3 s slghtly ncreased n followng step and calculaton starts wth ths ncreased concentraton of NH3. Calculaton becomes repettve. It s useful to engage teratve calculaton process, see fg.2. Varables wthout subscrpt correspond to state of the lqud mxture durng the saturaton process. Durng ths process, temperature, enthalpy and mass fracton of NH3 ncrease untl a termnal saturated state denoted by subscrpt 2. The teratve calculaton s stopped n the nstance when a dfference between enthalpy of the saturated mxture and enthalpy of the unsaturated mxture s smaller then a convergence crteron ε. The used equatons and approprate parameters are mentoned n the followng secton. Frst, the equaton for calculaton of saturated lqud mxture temperature s wrtten as functon of pressure and mole fracton of NH3 [1]: n m p0 T = T0 a ( x) ln 1 (5) p m n a , x , x , x , x , x , x , x , x , x , x , x , x , x , x 10-1 T 0 = 100 K p 0 = 2 MPa Table 1 Lst of parameters for equtaton (5)

3 Enthalpy of the saturated lqud mxture was calculated from equaton [1]: m T n 0 a x (6) T0 h = h 1 m n a , x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , x 10 1 h 0 = 100 kj/kg T 0 = 273,16 K Table 2 Lst of parameters for equtaton (6) Specfc thermal capacty [2] of the saturated lqud mxture was calculated wth utlzng of followng equatons: ( x) c ph O 3 1 (7) c p = x c pnh c p = Acp + Bcp τ (8) T τ 1 (9) T crt A cp B cp NH 3 3, , H 2 O 3, , Table 3 Lst of parameters for equtaton (8) The soluton crtcal temperature [3] was calculated wth utlzng of equaton: T crt = a x (10) 0 647, , , , , Table 4 Lst of parameters for equtaton (10) 3 Auxlary lnes formng Now we can start to draw the adabatc absorpton process n the p-t-x dagram. The unsaturated mxture s labeled as poston 1 n fg.3. We assume the sobarc absorpton process so saturatng soluton locatons must stay on a horzontal lne. Concentraton of NH3 and temperature of the soluton rse durng the absorpton a process. The termnal state of the soluton s shfted n rght hand drecton from the ntal poston. The fnal mxture parameters are easy to calculate wth the equatons mentoned above. Very useful s to have opportunty of obtanng the parameters drectly from the p-t-x dagram. Ths s useful for tme savng durng desgnng of new cycles. When we have been lookng for new adabatc absorpton auxlary lnes, we summarzed what parameters are requred for determnaton of the saturate state poston. Necessary nput parameters are mole fracton of NH3, temperature of the unsaturated state and correspondng pressure. The pressure and the temperature serve for determnaton of the ntal state p 100% NH 3 poston n the p-t-x dagram. Snce, concentraton lnes are drawn only for saturated states n the p-t-x dagram, poston of the unsaturated soluton s always located on left hand sde from the saturated soluton concentraton lne drawn for same mole fracton of NH3 as the unsaturated soluton mole fracton. Ths saturated soluton concentraton lne enables to estmate how far s the unsaturated soluton from ts saturated state. Two basc ponts defne an adabatc absorpton auxlary lne n p-t dagram. Frst pont corresponds to poston of the unsaturated mxture - pont 1. Second pont les on correspondng saturated mxture concentraton lne bellow poston of the termnal saturated state of mxture - pont 2 (obtaned from calculaton), see fg.4. The adabatc absorpton auxlary lnes show lnear character n p-t dagram of ammona - water system. Ths character was verfed by seres of calculatons. All adabatc absorpton auxlary lnes are parallel n p-t dagram. A schema of p-t-x dagram wth an adabatc absorpton auxlary lne s shown n fg.4. The auxlary lne utlzes the poston of an ntersecton wth the saturate soluton concentraton lne for determnaton of a termnal saturated soluton poston % 100% H 2 O Fg.3 Adabatc absorpton process n p-t-x dagram T

4 p 100% NH 3 50% 100% H 2 O adabatc absorpton auxlary lne T 2,x T 1 x 1 =50% Fg.4 Adabatc absorpton auxlary lne n p-t-x dagram Poston of the saturated lqud can be obtaned n four followng steps wth utlzng of an adabatc absorpton auxlary lne: 1. Draw the adabatc absorpton auxlary lne crossng the ntal unsaturated soluton (known p, T, x). 2. Determne an ntersectng poston of the adabatc absorpton auxlary lne and the saturate soluton concentraton lne for same T 3. concentraton as concentraton of the ntal unsaturated soluton. 4. Draw a vertcal lne upward from the ntersecton. 5. The termnal saturated soluton s located n an ntersecton of the vertcal lne and a correspondng sobarc lne (pressure of ntal unsaturated soluton). A fnal p-t-x dagram of ammona-water system wth four adabatc absorpton auxlary lnes s shown n fg.5. An example of usng of the adabatc absorpton auxlary lnes s drawn n ths fgure too. The auxlary lnes are lnear for mole fracton of NH3 from 100% tll 10%. Under 10% the auxlary lnes dvert from lnear character. The auxlary lnes are not drawn for mole fractons under 10% n the fg.5. Because t s not clear f ths behavor results from mxture physcal parameters or naccuracy of the used equatons. Detal analyss of ths behavor wll provde followng research. Fg.5 p-t-x dagram wth the adabatc absorpton auxlary lnes

5 4 Conclusons Ths paper ntroduces the new adabatc absorpton auxlary lnes n the p-t-x dagram of ammona-water system. These lnes serve for fast determnaton of the saturated state of mxture only wth knowledge of the unsaturated mxture parameters. The auxlary lnes assume absorpton of refrgerant saturated vapor at constant pressure. The paper ntroduces formng of the adabatc absorpton auxlary lnes wth utlzng of equatons for fast calculaton of ammona-water mxture propertes. Iteratve calculaton process was used for determnaton of saturated state. The new auxlary lnes help to estmate absorpton temperatures durng frst suggestons of an absorpton cycles. Correct determnaton of the absorpton temperatures lead to desgnng of cycles wth better absorpton heat utlzng. The paper shows practcal utlzng of the new auxlary lnes too. Acknowledgements: Ths work s part of research supported by the Mnstry of Educaton of the Czech Republc under the grant MSM and Mnstry of Industry and Trade of the Czech Republc under grant FF-P2/050. References: [1] J.Patek, J. Klomfar, 1995, Smple functons for fast calculatons of selected thermodynamc propertes of the ammona-water system, Int. J. Refrgeraton, 18(4), [2] Tllner-Roth, R.,D. G. Frend, 1998, Survey and Assessment of Avalable Measurements on Thermodynamc Propertes of the Mxtures, J. Phys. Chem. Ref. Data, 27(1), [3] Sassen, C. L., R.A.C. van Kwartel, H.J. van der Koo, J. de Swan Arons, 1990, Vapor - Lqud Equlbra for the System Ammona + Water up to the Crtcal Regon, j. Chem. Eng. Data, 35,