Aspen Physical Property System - Physical Property Models

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R = Gas constant T = Temperature nw = Kilograms of water mi With: 138 2 Thermodynamic Property Models = xi = Mole fraction of ion i xw = Mole fraction of water (molality of ion i) Mw = Molecular weight of water (g/mol) ni = Moles of ion i The function f(I) is an electrostatic term that expresses the effect of longrange electrostatic forces between ions. This takes into account the hard-core effects of the Debye-Hückel theory. This term is discussed in detail in the following section. The parameters �ij are second virial coefficients that account for the short-range forces between solutes i and j. The parameters �ijk account for the interactions between solutes, i, j, k. For ion-ion interactions, �ij is a function of ionic strength. For molecule-ion or moleculemolecule interactions this ionic strength dependency is neglected. The dependence of �ijk on ionic strength is always neglected. The matrices �ij and �ijk are also taken to be symmetric (that is, �ij = �ji). Pitzer modified this expression for the Gibbs energy by identifying combinations of functions. He developed interaction parameters that can be evaluated using experimental data. He selected mathematical expressions for these parameters that best fit experimental data. Pitzer's model can be applied to aqueous systems of strong electrolytes and to aqueous systems of weak electrolytes with molecular solutes. These applications are discussed in the following section. In the Aspen Physical Property System, this model is applied using the reference state of infinite dilution solution in water for non-water molecular solutes and ionic species. The properties such as DHAQFM are obtained at 25 C and 1 atm. Application of the Pitzer Model to Aqueous Strong Electrolyte Systems Pitzer modified his basic equation to make it more useful for data correlation of aqueous strong electrolytes. He defined a set of more directly observable parameters to represent combinations of the second and third virial coefficients. The modified Pitzer equation is:
zi = Charge of ion i Subscripts c, c', and a, a' denote cations and anions of the solution. B, C, �, and � are interaction parameters. f(I) is an electrostatic term as a function of ionic strength. The cation-anion parameters B and C are characteristic for an aqueous single-electrolyte system. These parameters can be determined by the properties of pure (apparent) electrolytes. B is expressed as a function of � (0) and � (1) , or of � (0) , � (2) , and � (3) (see equations 11 through 15). The parameters � and � are for the difference of interaction of unlike ions of the same sign from the mean of like ions. These parameters can be measured from common-ion mixtures. Examples are NaCl + KCl + H2O or NaCl + NaNO3 + H2O (sic, Pitzer, 1989). These terms are discussed in detail later in this section. Fürst and Renon (1982) propose the following expression as the Pitzer equation for the excess Gibbs energy: The difference between equations 3 and 4 is that Pitzer orders cation before anions. Fürst and Renon do not. All summations are taken over all ions i and j (both cations and anions). This involves making the parameter matrices Bij, Cij, �ij, and �ijk symmetric, as follows: Second-order parameters are written Bij if i and j are ions of different sign. Bij = 0 if the sign of zi = sign of zj, and Bii = 0. Since cations are not ordered before anions, Bij = Bji. This eliminates the 2 in the second term in brackets in Pitzer's original expression (equation 3). Second-order parameters are written �ij if i and j are ions of the same sign. Thus �ij = 0 if the sign of zi is different from the sign of zj, and �ii = 0 with �ij = �ji. Third-order parameters are written Cij if i and j are ions with different signs. Cij = 0 if the sign of zi = sign of zj, and Cii = 0 with Cij = Cji. The factor of 2 in the fifth bracketed term in Pitzer's original expression (equation 3) becomes 1/2 in equation 4. The matrix C is symmetric and is extended to all ions to make the equation symmetric. 2 Thermodynamic Property Models 139 (3) (4)
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Aspen Physical Property System Phys
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Contents Contents..................
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General Pure Component Solid Molar
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1 Introduction This manual describe
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Pure Component Temperature- Depende
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the Properties Parameters Pure-Comp
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2 Thermodynamic Property Models Thi
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Property Model Model Name Phase(s)P
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Property Model Model Name 2 Thermod
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Where: Parameter Name/Element 2 The
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critical temperature, the critical
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Where the ideal-gas contribution
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, where � For polar, associating
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Parameter Name/ Element 2 Thermodyn
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The denominator of equation 8 is gi
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V. V. De Leeuw and S. Watanasiri, "
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References M. Benedict, G. B. Webb,
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References L. Haar, J.S. Gallagher,
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Parameter Name/Element NTHDDH 0 †
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Gibbs free energy departure: The fo
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For a block copolymer, there is onl
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Copolymer PC-SAFT Dispersion Term T
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The association-site number of the
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Then I2(�) and I3(�) are comput
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A databank called PC-SAFT contains
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Parameter Name/Element PRKBV/1 k ij
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Predictive SRK (PSRK) This model us
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ka,ij kb,ij = = For best results, b
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J. Schwartzentruber and H. Renon, "
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Redlich-Kwong-Soave-MHV2 This equat
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‡ RKUC0, RKUC1, and RKUC2 are tre
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Parameter Name/ Element SRKLIJ/3 l
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Parameter Name/ Element Symbol Defa
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Association Equilibria Every associ
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and respectively. For the reactions
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R. W. Long, J. H. Hildebrand, and W
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Where the L, M, and N are parameter
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Alpha function Model name First Opt
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mi = Computed by equation 6 Equatio
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Parameter Name/Element 2 Thermodyna
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standard RKS alpha function, except
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These mixing rules are discussed se
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Where both Ai* and Am are calculate
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Like Huron and Vidal, the limiting
Page 89 and 90: Model Type Wilson Local composition
Page 91 and 92: Therefore, the simplified Pitzer eq
Page 93 and 94: Parameter Name/Element Symbol Defau
Page 95 and 96: Where: �i 2 Thermodynamic Propert
Page 97 and 98: The electrolyte NRTL model uses the
Page 99 and 100: Parameter Symbol No. of Name Elemen
Page 101 and 102: with Where: xi = Mole fraction of c
Page 103 and 104: It should be understood that equati
Page 105 and 106: The reference Gibbs energy is deter
Page 107 and 108: Where: j and k can be any species (
Page 109 and 110: The pure component dielectric const
Page 111 and 112: 2 Thermodynamic Property Models 109
Page 113 and 114: �I *PDH = Pitzer-Debye-Hückel te
Page 115 and 116: Where: �i Vi = Activity coefficie
Page 117 and 118: Recommended cij Values for Differen
Page 119 and 120: Parameter Name/ Element 2 Thermodyn
Page 121 and 122: NRTL-SAC Reference States The NRTL-
Page 125 and 126: For an anionic component, we have M
Page 127 and 128: For a molecular segment, the activi
Page 129 and 130: Specifically, The long range intera
Page 131 and 132: where and are activity coefficients
Page 133 and 134: and Y+, are used to reflect the wid
Page 135 and 136: Parameter Name/ Element Symbol Defa
Page 137 and 138: Reference C.-C. Chen and Y. Song, "
Page 139: Parameter Name GMPTPS, GMPTP1, GMPT
Page 143 and 144: For option code = 0 (default), the
Page 145 and 146: and for n-m electrolytes: 2 Thermod
Page 147 and 148: = 0.00979 Perform the necessary con
Page 149 and 150: Pitzer, K.S., J.R. Peterson, and L.
Page 151 and 152: A4,ij = gij / T + hij A5,ij = mij /
Page 153 and 154: Symmetric and Unsymmetric Electroly
Page 155 and 156: Parameter Symbol No. of Name Elemen
Page 157 and 158: Reference state for ionic component
Page 159 and 160: with 2 Thermodynamic Property Model
Page 161 and 162: G for these pairs is calculated the
Page 163 and 164: with 2 Thermodynamic Property Model
Page 167 and 168: Activity Coefficient Basis for Henr
Page 169 and 170: Where is the liquid Gibbs free ener
Page 171 and 172: Ionic components 2 Thermodynamic Pr
Page 173 and 174: the pure fused salts. Applying Eq.
Page 175 and 176: �k is the activity coefficient of
Page 177 and 178: References U. Weidlich and J. Gmehl
Page 179 and 180: ti' = �ij 2 Thermodynamic Propert
Page 181 and 182: Wagner Interaction Parameter The Wa
Page 183 and 184: References G.M. Wilson, J. Am. Chem
Page 185 and 186: Extended Antoine Equation Parameter
Page 187 and 188: IK-CAPE Vapor Pressure Equation The
Page 189 and 190: Harlacher and Braun, "A Four-Parame
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General Pure Component Heat of Vapo
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IK-CAPE Heat of Vaporization Equati
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Where: xp = Mole fraction of pseudo
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Parameter Name/Element VLBROC/1 V i
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Where: Vm l,t = Liquid volume per n
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Debye-Hückel Volume The Debye-Hüc
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DIPPR DIPPR equation 105 is the def
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Rackett The Rackett equation is: Wh
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Rackett/Campbell-Thodos Mixture Liq
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Zm RA Zi *,RA Vcm 2 Thermodynamic P
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General Pure Component Solid Molar
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Liquid Volume Quadratic Mixing Rule
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If THRSWT/6 is This equation is use
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Parameter Symbol Default MDS Lower
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General Pure Component Ideal Gas He
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(Other DIPPR equations may sometime
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General Pure Component Solid Heat C
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The expression for the liquid mole
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� Entropy: � Heat capacity: �
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Parameter Name † /Element CPIXPn/
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Option Codes for Electrolyte NRTL E
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Parameter Name Applicable Component
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For subcritical components: Hm l -H
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The vapor enthalpy is calculated fr
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Where: 2 Thermodynamic Property Mod
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Correlation algorithms for ionic sp
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Model Model name Phase(s) Pure Mixt
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Model Type Aspen Liquid Mixture Vis
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(Other DIPPR equations may sometime
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�i = Viscosity of component i (N-
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Parameter Name/Element 3 Transport
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Where: The Stockmayer or Lennard-Jo
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Where: Vcij = �ij = 0 (in almost
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Where: Vcij = �ij = 0 (in almost
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Jones-Dole Electrolyte Correction T
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Letsou-Stiel The Letsou-Stiel model
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Where: The parameter is the mole fr
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Reference C.H. Twu, "Internally Con
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Vcij 3 Transport Property Models 27
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You must provide parameters for the
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Linear extrapolation of � *,l ver
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If TRNSWT/4 is This equation is use
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References R.C. Reid, J.M. Prausnit
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The mixture surface tension is then
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Where: �solv = Dielectric constan
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4 Nonconventional Solid Property Mo
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wij = Mass fraction of the jth cons
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The oxygen and organic sulfur conte
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Parameter Name/Element Symbol Defau
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The complete oxidation of carbon is
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Parameter Name/Element Symbol Defau
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The equation for �i dm is good fo
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5 Property Model Option Codes The f
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Model Name Option Code 5 Property M
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Model Name Option Code 5 Property M
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Soave-Redlich-Kwong Option Codes Th
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Model Name Option Code HLRELNRT and
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Model Name Option Code GLRELNRT, GL
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Index A activity coefficient models
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ideal gas/DIPPR heat capacity model
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S Sato-Riedel/DIPPR thermal conduct
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Aspen Physical Property System - Physical Property Models

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