The ChemSep Book Harry A. Koojman Consultant Ross Taylor Clarkson Unversty, Potsdam, New York Unversty of Twente, Enschede, The Netherlands Lbr Books on Demand www.bod.de
Copyrght c 2000 by H.A. Koojman and R. Taylor. All rghts reserved. Errata from ISBN 3-8311-1068-9
13.1.7 Enthalpy The mxture enthalpy can be calculated from the component enthalpes wth: 330 H = c z H (13.1) =1 where z s the mole fracton of speces n the phase n queston. The component enthalpy may be expressed as the sum of the deal contrbuton and an excess enthalpy: H = H d where H ex s the excess enthalpy and H d enthalpy of component s gven by: T H g,d = T 0 C g,d p, + H ex (13.2) s the deal contrbuton. The deal gas dt + H298K form, (13.3) where Cp, d s the deal gas heat capacty of component, T 0 s a reference temperature, Hform, 298K the enthalpy of formaton at 298 K, and T s the actual temperature at whch the enthalpy s to be calculated Note that there s no composton dependence n the deal gas enthalpy! The enthalpy of formaton are only ncluded when reactons are present. Ths s done because the enthalpes of formaton are large compared to the other contrbutons and ths makes the enthalpy balance less accurate. Also note that enthalpes are computed relatve to a reference pont, 0, and are not absolute! Normally, ths reference pont for the enthalpy n ChemSep s chosen as an deal gas at 298 K. However, the reference state and temperature as well as the ncluson of heat of formatons can be changed n the References menu under the propertes selecton. For lquds, the latent heat of vaporzaton s subtracted from the deal gas enthalpy: H l,d = H g,d H vap (13.4) where H vap s computed wth a temperature correlaton (see the secton on physcal propertes below) or, f no correlaton parameters are known, usng the method of Ptzer et al.: H vap = RT c, (7.08(1 T r, ) 0.354 + 10.95(1 T r, ) 0.456 ω ) (13.5) If an equaton of state model s used for the K-values n ChemSep, the excess enthalpy of both phases s calculated from an equaton of state as follows: ( ) ln H ex = RT 2 φ (13.6)
If an actvty coeffcent model s used for the lqud phase, then the component excess enthalpy s computed from: H ex ( ) ln = RT 2 γ ChemSep ncorporates the followng methods for estmatng the enthalpy: (13.7) None No enthalpy balance s used n the calculatons. WARNING: the use of ths model wth subcooled and superheated feeds or for columns wth heat addton or removal on some of the stages wll gve ncorrect results. The heat dutes of the condenser and reboler wll be reported as zero snce there s no bass for calculatng them. Ideal (B152) In ths model the enthalpy s computed from the deal gas contrbuton and the excess enthalpy s assumed to be zero. Excess (B518) Ths model ncludes the deal enthalpy as above. The excess enthalpy s calculated from the actvty coeffcent model or the temperature dervatve of the fugacty coeffcents dependent on the choce of the model for the K-values, and s added to the deal part. Polynomal vapor as well as lqud enthalpy are calculated as functons of the absolute temperature (K). Both the enthalpes use the followng functon: H = A + B T + C T 2 + D T 3 (13.8) You must enter the coeffcents A through D n the Load Data opton of the Propertes menu for vapor and lqud enthalpy for each component. 13.1.8 Entropy The mxture entropy can be calculated from the component entropes n a smlar manner as the enthalpy: c S = z S (13.9) =1 where z s the mole fracton of speces n the phase n queston. The component entropy may be expressed as the sum of the component entropy plus the contrbutons of deal and excess mxng entropy: S = S d + S ex (13.10) 331
where S ex s the excess entropy and S d s the deal contrbuton for component. The deal gas entropy of component s gven by: T S d,g = S 0, + T 0 g,d C p, T ( p dt R ln p 0 ) R ln z (13.11) where C d p, s the deal gas heat capacty of component, T 0 s the reference temperature, p 0 the reference pressure, S 0, the absolute entropy of component at T 0 and p 0, z the mole fracton of, and T and p are the actual temperature and pressure at whch the entropy s to be calculated. The reference pont for entropy s fxed at 298 K and 1 atm because the absolute component entropes are defned at ths temperature and pressure. These component absolute entropes are stored n the pure component database. For the deal lqud entropy we subtract the entropy of vaporzaton: S d,l = S d,g H vap, T bol (13.12) where H vap, s the vaporzatons enthalpy of component at T bol, the component normal bolng temperature. Excess mxture entropes are computed wth ( S ex = R T ln γ ) + ln γ (13.13) when an actvty coeffcent model s used. If an equaton of state s used γ s replaced by φ, the fugacty coeffcent of. 13.1.9 Exergy The exergy (Ex) of a mxture or stream can be calculated from the enthalpy and entropy wth Ex = H T surr S (13.14) where T surr s the surroundngs temperature of the process (ths temperature s normally set to 298 K but can be changed under the References menu n the propertes selecton). Note that wth the ncluson of the enthalpy, the exergy n ChemSep s also a relatve quantty wth respect to the enthalpy reference pont. Exergy s sometmes also referred to as avalablty, t ndcates the work that can be extracted from a stream that s brought to equlbrum wth ts surroundng state. Therefore, exerges provde useful nsghts n the thermodynamc effcency of processes. The second law of thermodynamcs states that for any real, rreversal process there s a nett entropy producton ( S rr ), for whch work (ether drect or ndrect n the form of exergy) s lost. The lost work equals T o S rr and the hgher ths amount relatve to the work/exergy nput, the lower s the thermodynamc effcency. 332