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Preparation of Psychrometric Charts for Alcohol Vapours in Nitrogen

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Preparation of Psychrometric Charts for Alcohol Vapours in Nitrogen Korean J. Chem. Eng., 17(1), 93-100 (2000) Preparation of Psychrometric Charts for Alcohol Vapours in Nitrogen David C. Shallcross† Department of Chemical Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia (Received 30 September 1999 • accepted 27 October 1999) Abstract−Psychrometric charts for three different systems involving condensing alcohol vapour in nitrogen are presented. The alcohols considered are methanol, ethanol and n-propanol. The charts are based upon semi-the- oretical equations and make use of published physical property data and correlations. The behaviour of the vapour phase is characterised by the Virial Equation of State truncated at the third term. The solubility of nitrogen in the liquid alcohols is also considered. The charts are constructed with the dry bulb temperature and absolute humidity scales as the orthogonal axes. Curves of constant adiabatic saturation temperature, constant relative humidity, con- stant gas specific volume and constant enthalpy deviation are plotted on the charts. Key words: Psychrometry, Humidity, Virial Equation, Alcohol ˆ INTRODUCTION where, PT is the total pressure, V is the molar volume of the gas mixture, R is the gas constant, T is the absolute temperature, For any system in which one or more components of a gase- and Bm and Cm are the second and third virial coefficients of the ous mixture may condense, engineering requires the ability to gas, respectively. predict the conditions and extent to which condensation will In the development of the equations which follow we shall occur. Even in this age of computer-aided design and physical assume that there are only two components in our system. The property databases, engineers still find it useful to have physi- vapour component that readily condenses will be denoted V, cal property data presented graphically. Psychrometric charts are and the gas component will be denoted G. a way in which physical property data may be presented dia- If xG is the mole fraction of the non-condensing component grammatically for systems in which one component of a gas- (in this case nitrogen) and xV is the mole fraction of the con- eous mixture may condense. While accurate charts are readily densing component (i.e., the alcohol), then for a binary system available for the conventional water-air system, only recently it may be shown that: have charts been prepared for other important systems. Just as = 2 + + 2 importantly, until recently [Shallcross, 1997] few charts had Bm xGBGG 2xGxVBGV xVBVV (2) been prepared for pressure other than atmospheric. 3 2 2 3 Cm = xGCGGG +++3xGxVCGGV 3xGxVCGVV xVCVVV (3) The author [Shallcross and Low, 1994, 1996; Shallcross, 1997] has described the theory behind the construction of psychromet- Here Bii is the second virial coefficient of pure component i, ric charts. In this paper this method will be applied to construct BGV is the second virial interaction (or cross) coefficient for the a series of psychrometric charts for alcohol vapours in nitrogen. binary system, Ciii is the third virial coefficient of pure compo- The alcohols considered are methanol, ethanol and n-propanol. nent i, and, CGGV and CGVV are the third virial interaction param- eters. The virial coefficients are all functions of temperature GAS PHASE BEHAVIOUR AND SATURATION alone, and are either known or may be estimated for most binary systems. At even relatively low pressures the gas mixture of nitrogen A gas is saturated with a vapour when the partial pressure of and the liquid alcohols will not behave ideally. From the many the vapour is equal to its vapour pressure at the particular tem- different methods by which the non-ideal behaviour of gas may perature. For an ideal system we could write an expression be characterized, the Virial Equation of State is used. This method relating the mole fraction of the condensing vapour component is relatively simple to apply and considerable data is available at saturation, V, to its vapour pressure: for the required parameters for each of the systems studied. P =----V- xVS (4) The Virial Equation of State truncated at the third term is: PT P Vˆ B C and ---------T =1+-----m-+-----m- (1) RT Vˆ ˆ 2 P −P V =-------------T V- xGS (5) PT †To whom correspondence should be addressed. E-mail: [email protected] where, xVs and xGs are the mole fractions of components V and This paper was presented at the 8th APCChE (Asia Pacific Confedera- G, respectively, at saturation, and PV is the vapour pressure of tion of Chemical Engineering) Congress held at Seoul between August component V. However, since the system is not ideal Hyland 16 and 19, 1999. and Wexler [1983] proposed the use of an enhancement factor. 93 94 D. C. Shallcross Eq. (4) becomes, a psychrometric chart for a system may be calculated using the Virial Equation and the enhancement factor to account for the fP x =-------V (6) non-idealities in the system. The psychrometric charts are con- Vs P T structed with temperature plotted on the x-axis and absolute A similar expression may be written for the non-condensing humidity on the orthogonal y-axis. The saturation line that de- gas component G: scribes the boundary of the humidity chart is drawn by plotting − the absolute humidity at saturation, Hs, as a function of temper- =PT fPV xGs ---------------- (7) ature for a specified total pressure. Series of curves for constant P T relative humidity, constant specific volume and constant adia- The enhancement factor accounts for the effects of the dissolv- batic saturation temperature may be generated by use of the ed gases and pressure on the properties of the condensed phase, equations presented. and the effect of intermolecular forces on the properties of the The relative humidity, φ, is defined as the ratio of the mole moisture itself. Typically, the value for the enhance factor does fraction of the vapour component, xV , in a given sample of the not exceed 1.05 for any given system [Shallcross, 1996]. The two-component mixture to the mole fraction, xVs, in a sample of enhancement factor may be written in terms of the virial coeffi- the mixture which is saturated with the vapour component at cients and other properties of the system [Hyland and Wexler, that temperature. Thus, 1983]: x φ=------V (10) xVs + − −1 2− 2 ()1 κPV ()PT PV ---κ()PT PV = 2 ˆ + − In order to construct the curves of constant relative humidity lnf -------------------------------------------------------------------- VVc ln()1 kHxGsPT RT an expression is required which relates the absolute humidity to 3 ()− 2 2 2 the relative humidity, temperature and total pressure. Shallcross − 2xGs 2 3xGs PT +xGsPT −2xGsPT ------------------------------------ B B ------------B ---------------B [1997] derives the equation: ()RT 2 GG GV RT GG RT GV H φ()1−fP ⁄P − − 2 2 ()− ()− 2 =----------------------------------s V T- − PT PV xGsPT −xGs 1 3xGs 1 xGs PT H −φ ⁄ (11) ------------------------------ B ---------------------------------------------------B B 1 fPV PT RT GG ()RT 2 GG VV 2 2 2 2 2 To construct the constant relative humidity curves, the system 6xGs()1−xGs PT 2xGs()1−xGs ()1−3xGs PT 2 + − -----------------------------------BVVBGV ------------------------------------------------------ BGV pressure, P , is first specified. Then for a given value of φ, the ()RT 2 ()RT 2 T variables f, H and P are calculated for varying temperatures. 2 −()+ ()− 3 2 4 2 s v − PV 1 3xGs 1 xGs PT 2 − 3xGsPT 2 These values are then used in Eq. (11) to calculate the absolute ------------------------------------------------------2 - BVV -----------------2BGG 2RT() 2RT() humidity as a function of temperature. When plotted, this data 2 ()+ 2 2 ()− 2 + 3xGs 1 2xGs PT −3xGs 1 xGs PT yields the constant relative humidity curves. ------------------------------------ CGGV ---------------------------------CGVV 2RT()2 ()RT 2 The specific volume of a humid mixture, ν, is defined as the ()+ ()− 2 2− 2 3 2 volume of the mixture per unit mass of the dry gas: 1 2xGs 1 xGs PT PV xGsPT − ------------------------------------------------------- + ------------- 2 CVVV 2CGGG (8) 2RT() ()RT Vˆ ν=------------------- (12) Here κ is the iso-thermal compressibility of the condensing com- xGMWG ponent (i.e., the hydrocarbon), VVc is the molar volume of the Applying this definition and using Eq. (1), Shallcross [1997] shows condensed component V (either as a liquid or a solid), and kH is how the curves of constant specific volume may be plotted for the Henry's Law constant to account for the solubility of com- a given system pressure. ponent G in the condensed phase. For a given temperature and The wet bulb temperature is usually considered as the tem- total pressure, PT, Eq. (7) and (8) may be solved iteratively for perature measured by a cylindrical thermometer, the outside sur- the enhancement factor, f, and the mole fraction of component face of which is kept wet with the liquid of the condensing com- = G at saturation, xGs. In practice this is done by first setting f 1. ponent V. As the moist gas passes the thermometer some of the xGs is then calculated by using Eq. (7), and then this value is liquid evaporates resulting in a cooling effect that causes the tem- used in Eq. (8) to calculate an estimate for the enhancement fac- perature of the wet bulb thermometer to drop. The drier the gas, tor, f. The value for xGs is then recalculated. The cycle is then the greater the wet bulb depression. It is not possible to predict repeated until the values for f and xGs no longer change signifi- the wet bulb temperatures with precision, because the wet bulb cantly between successive calculations. temperature is a function of not only the dry bulb temperature The absolute humidity at saturation, Hs, is the mass of the and absolute humidity, but also such factors as the gas velocity vapour component V per mass of component G.
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