Transcript Thermodynamic Property Methods

Ref: Physical Property Methods and Models, Aspen Technology, Inc., 2006
1
Property Methods
 A property method is a collection of property calculation routes.
 Thermodynamic properties:
• Phase equilibrium (VLE, LLE, VLLE)
• Enthalpy
• Entropy
• Gibbs free energy
• Molar volume
 Transport properties:
• Viscosity
• Thermal conductivity
• Diffusion coefficient
• Surface tension
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Property Methods
 It is important to choose the right property method for an
application to ensure the success of your calculation.
 The classes of property methods available are:
• IDEAL
• Liquid fugacity and K-value correlations
• Petroleum tuned equations of state
• Equations of state for high pressure hydrocarbon applications
• Flexible and predictive equations of state
• Liquid activity coefficients
• Electrolyte activity coefficients and correlations
• Solids processing
• Steam tables
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EOS Method
1- Vapor-Liquid Equilibrium
fi  fi
v
 At Equilibrium:
 Where
 Therefore
fi   y P ,
v
v
i i t
l
fi   x P
l
l
i i t
yi 
k  
xi 
vl
i
l
i
v
i
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EOS Method
2- Liquid-Liquid Equilibrium
fi  fi
l1
 At Equilibrium:
 Where
 Therefore
fi   x P ,
l1
l1 l1
i i t
k
l1l2
i
l2
fi   x P
l2
l2 l2
i
i t
x



x

l1
i
l2
i
l2
i
l1
i
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EOS Method
3- Vapor-Liquid-Liquid Equilibrium
fi  fi  fi
l1
 At Equilibrium:
l2
v
f i   x P , f i   x Pt
f  iv yi Pt
l1
 Where
 Therefore
k
vl1
i
l1 l1
i i t
v
i
yi 
 l1 
xi

l1
i
v
i
l2
, k
l2
i
vl2
i
l2
i
yi 
 l2 
xi

l2
i
v
i
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EOS Method
4- Fugacity Coefficient Formula


V  P 
1
RT





ln i  

dV

ln
Z
m




RT
 ni T ,V ,n j V 


Cubic Equations of State in the Aspen Physical Property System
Redlich-Kwong(-Soave) based
Peng-Robinson based
Redlich-Kwong (RK)
Standard Peng-Robinson(PENG-ROB)
Standard Redlich-Kwong-Soave(RK-SOAVE ) Peng-Robinson(PR-BM)
Redlich-Kwong-Soave (RKS-BM)
Peng-Robinson-MHV2
Redlich-Kwong-ASPEN(RK-ASPEN)
Peng-Robinson-WS
Schwartzentruber-Renon
Redlich-Kwong-Soave-MHV2
Predictive SRK (PSRK)
Redlich-Kwong-Soave-WS
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EOS Method
5- Standard RK-SOAVE
RT
a
P

Vm  b Vm (Vm  b)
 Where
a   xi x j (ai a j )0.5 (1  kij ), b   xibi
i
j
i
R 2Tci2
RTci
ai   i 0.42747
, bi  0.08664
Pci
Pci
i (T )  [1  mi (1  Tri0.5 )]2 , mi  0.481.57i  0.176i2
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EOS Method
6- Standard PENG-ROB
RT
a
P

Vm  b Vm (Vm  b)  b(Vm  b)
 Where
a   xi x j (ai a j )0.5 (1  kij ), b   xibi
i
j
i
R 2Tci2
RTci
ai   i 0.45724
, bi  0.07780
Pci
Pci
i (T )  [1  mi (1  Tri0.5 )]2 , mi  0.374641.54226i  0.26992i2
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EOS Method
7- Advantages and Disadvantages
 Equations of state can be used over wide ranges of
temperature and pressure, including subcritical and
supercritical regions.
 Thermodynamic properties for both the vapor and liquid
phases can be computed with a minimum amount of
component data.
 For the best representation of non-ideal systems, you must
obtain binary interaction parameters from regression of
experimental VLE data. Binary parameters for many
component pairs are available in the Aspen databanks.
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EOS Method
7- Advantages and Disadvantages…
 Equations
of state are suitable for modeling
hydrocarbon systems with light gases such as CO2 , N2
and H2 S .
 The assumptions in the simpler equations of state
(SRK, PR, Lee-Kesler , … ) are not capable of
representing highly non-ideal chemical systems, such
as alcohol-water systems. Use the activity-coefficient
options sets for these systems at low pressures. At high
pressures, use the predictive equations of state.
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Activity Coefficient Method
1- Vapor-Liquid Equilibrium
fi  fi
v
 At Equilibrium:
 Where
fi v  iv yi Pt ,
l
fi l   i xi fi*,l
yi  i f i
k   v
xi
i Pt
*,l
 Therefore
vl
i
 F0r ideal gas and liquid
*
y
P
v
vl
 i  1, i  1  ki  i  i Raoult' s Law
xi Pt
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Activity Coefficient Method
2- Liquid-Liquid Equilibrium
fi  fi
l1
 At Equilibrium:
 Where
 Therefore
fi   x f
l1
l1 l1 *,l
i i i
k
l1l2
i
,
l2
fi   x fi
l2
x



x

l1
i
l2
i
l2 l2
i i
*,l
l2
i
l1
i
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Activity Coefficient Method
3- Vapor-Liquid-Liquid Equilibrium
 At Equilibrium:
 Where
fi  fi  fi
l1
l2
v
fi   x fi
, fi   x fi
f i v  iv yi Pt
l1
 Therefore
k
vl1
i
l1 l1
i i
l2
*,l
yi  f i
 l1  v
xi
i Pt
l1
i
l2
i
*,l
, k
vl2
i
l2
i
*,l
yi  f i
 l2  v
xi
i Pt
l2
i
*,l
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Activity Coefficient Method
4- Liquid Phase Reference Fugacity
 For solvents: The reference state for a solvent is defined as
pure component in the liquid state, at the temperature and
pressure of the system.
fi   (T , Pi )Pi q , ( i 1 as xi 1)
*,l
*,v
i
*,l
*,l
*,l
i
 i*,v = Fugacity coefficient of pure component i at the system
temperature and vapor pressures, as calculated from the vapor phase
equation of state
 qi*,l = Poynting factor
q
*,l
i
 1 P *,l 
 exp
Vi dP
*,l

 RT Pi

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Activity Coefficient Method
4- Liquid Phase Reference Fugacity
 For dissolved gases: Light gases (such as O2 and N2 ) are
usually supercritical at the temperature and pressure of the
solution. In that case pure component vapor pressure is
meaningless and therefore it cannot serve as the reference
fugacity.
fi l  xi  i* Hi
and  i* 1 as xi  0
 Using an Empirical Correlation: The reference state fugacity
is calculated using an empirical correlation. Examples are the
Chao-Seader or the Grayson-Streed model.
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Activity Coefficient Method
5- Multicomponent Mixtures
 Multicomponent vapor-liquid equilibria are calculated from
binary parameters. These parameters are usually fitted to binary
phase equilibrium data (and not multicomponent data) and
represent therefore binary information. The prediction of
multicomponent phase behavior from binary information is
generally good.
 Multi-component liquid-liquid equilibria cannot be reliably
predicted from binary interaction parameters fitted to binary
data only. In general, regression of binary parameters from
multi-component data will be necessary.
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Activity Coefficient Method
6- NRTL (Non-Random Two-Liquid)
 The NRTL model calculates liquid activity coefficients for the
following property methods: NRTL, NRTL-2, NRTL-HOC,
NRTL-NTH, and NRTL-RK. It is recommended for highly
nonideal chemical systems, and can be used for VLE, LLE and
VLLE applications.
x  G

x G
j
ln  i
ji
j
k
k
ki
ji


xm mj Gmj

 x j Gij 
m
 


 ij
x
G
xk Gkj
j   k kj 

k

 k





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Activity Coefficient Method
6-NRTL (Non-Random Two-Liquid)
x  G

x G
j
ln  i
ji
j
k
k
 Where
ki
ji


xm mj Gmj

 x j Gij 
m
 
 ij 
xk Gkj
j   xk Gkj 

k

 k





Gij  exp( ij ij ) , Gii  1
 ij  aij  bij T  eij ln T  f ijT ,  ii  0
 ij  cij  d ij (T  273.15)
 The binary parameters aij, bij, cij, dij, eij and fij can be determined
from VLE and/or LLE data regression. The Aspen Physical Property
System has a large number of built-in binary parameters for the
NRTL model.
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Activity Coefficient Method
7- Advantages and Disadvantages
 The activity coefficient method is the best way to represent
highly non-ideal liquid mixtures at low pressures.
 You must estimate or obtain binary parameters from
experimental data, such as phase equilibrium data.
 Binary parameters are valid only over the temperature and
pressure ranges of the data.
 The activity coefficient approach should be used only at low
pressures (below 10 atm).
 The Wilson model cannot describe liquid-liquid separation at
all; UNIQUAC, UNIFAC and NRTL are suitable.
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Principle Steps in Selecting the Appropriate
Property Method
1. Choosing the most suitable property method.
2. Comparing the obtained predictions with data from
the literature.
3. Estimate or obtain binary
experimental data if necessary.
parameters
from
4. Generation of lab data if necessary to check the
property model.
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Eric Carlson’s Recommendations
Figure 1
Polar
Non-electrolyte
See Figure 2
E?
Electrolyte NRTL
Or Pizer
Electrolyte
Real
All
Non-polar
Peng-Robinson,
Redlich-Kwong-Soave,
Lee-Kesler-Plocker
R?
Polarity
R?
Real or
pseudocomponents
P?
Pressure
E?
Electrolytes
Pseudo & Real
P?
Vacuum
Chao-Seader,
Grayson-Streed or
Braun K-10
Braun K-10 or ideal
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Yes
Figure 2
Yes
P < 10 bar
(See also
Figure 3)
P?
NRTL, UNIQUAC
and their variances
LL?
WILSON, NRTL,
UNIQUAC and
their variances
No
ij?
Yes
No
LL?
Polar
Non-electrolytes
No
Yes
LL? Liquid/Liquid
P?
Pressure
ij?
Interaction Parameters
Available
P > 10 bar
UNIFAC LLE
UNIFAC and its
extensions
Schwartentruber-Renon
PR or SRK with WS
PR or SRK with MHV2
ij?
No
PSRK
PR or SRK with MHV2
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Hexamers
Figure 3
Yes
DP?
Dimers
VAP?
Wilson
NRTL
UNIQUAC
UNIFAC
VAP?
DP?
Wilson, NRTL, UNIQUAC,
or UNIFAC with special EOS
for Hexamers
No
Wilson, NRTL, UNIQUAC,
UNIFAC with Hayden O’Connell
or Northnagel EOS
Wilson, NRTL,
UNIQUAC, or UNIFAC*
with ideal Gas or RK EOS
Vapor Phase Association
Degrees of Polymerizatiom
UNIFAC* and its Extensions
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Eric Carlson’s Recommendations
for 1-Propanol ,H2O mixture
Figure 1
Non-electrolyte
Polar
See Figure 2
E?
Polarity
R?
Real or
pseudocomponents
P?
Pressure
E?
Electrolytes
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Figure 2
Yes
P < 10 bar
(See also
Figure 3)
P?
Polar
Non-electrolytes
LL?
WILSON, NRTL,
UNIQUAC and
their variances
No
ij?
No
LL?
No
UNIFAC and its
extensions
LL? Liquid/Liquid
P?
Pressure
ij?
Interaction Parameters
Available
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