OLI-MSE Data Regression
Additional course materials can be found at:
http://support.olisystems.com/
MSE fundamentals:
P. Wang, A. Anderko, R. D. Young; Fluid Phase Equilbria,
2002, 203, 141-176
P. Wang, R. D. Spinger, A. Anderko, R. D. Young; Fluid
Phase Equilbria, 2004, 222-223, 11-17
P. Wang, A. Anderko, R. D. Spinger, R. D. Young; Journal of
Molecular Liquids, 2006, 125,37-44
OLI-MSE Data Regression
Objectives
• To create new model parameters
• To obtain improved model parameters
• To reevaluate model parameters using new
or proprietary data
 To accurately reproduce experimental
results
OLI-MSE Data Regression
Steps
• Collecting relevant literature data
• Customizing chemistry model
• Preparing regression input file
• Running the regression
• Reviewing regression output
Types of thermophysical data
used in MSE regression
•
•
•
•
•
•
•
•
Water activity or osmotic coefficients
Vapor pressure (VLE)
Solubility (SLE)
Solubility (LLE)
Speciation (pH, dissociation degree, etc)
Density
Enthalpy (Hdil and Hmix)
Heat capacity
Model Parameters
Chemical & phase
equilibrium
calculations require
Model Parameters
Standard state properties
Gref, Sref, Cp, and
HKF parameters
Excess properties
Activity coefficient
model parameters
MSE Model: Excess Gibbs Energy
ex
G
RT
LR
LC
MR
ex
ex
ex
G
G LR
G

 LC  MR
RT
RT
RT
Debye-Hückel theory
Local composition model (UNIQUAC) for neutral
molecule interactions
Ionic interaction term for ion-ion and ion-molecule
interactions
ex

 G
ln  k 
nk  RT



T , P , n j , j  k
MSE Model:
Long-range electrostatic interaction
(Debye-Hückel) term

12

4
A
I
1


I

 x x
x
   ni 
ln 
RT
i  
  xi [1   I x0,i
 i
ex
G DH



12
]

 
A function of ionic strength and solvent properties
No interaction parameters
MSE Model:
Neutral molecule interaction term –
Local composition model (UNIQUAC)
ex
GUNIQUAC
RT
ex
ex
Gcombinator
G
ial

 residual
RT
RT
ex

Gcombinator
i Z
i 


ial
   n i  xi ln   qi xi ln 
RT
xi 2 i
i 
 i  i
Parameters -
ex



Gresidual


   n i  q i xi ln   j ij 
RT
 i  i
 j

• Species specific: R (size) and Q (surface area)
• Interaction: aij and aji
MSE Model:
Ionic interaction (Middle-Range) term
ex


G MR
   ni  xi x j Bij I x 


RT
 i
 i j
Bij I x   bij (T )  cij (T ) exp( I x  a1 )
Interaction Parameters bij and cij
MSE Databank:
MSEPUB
• Equivalent to PUBLIC for
OLI/Aqueous framework
• H3OION-based databank
– reactions are balanced using H3OION
and H2O instead of using HION and
H2O
MSE Databank: MSEPUB
Data items specifically used by MSE model
In “Aqueous Phase” chapter
Pure Liquid Properties (for organic molecules)
LDEN – Coefficients for pure liquid molar density
 kmol / m  
A
3
1 (1T / C ) D
B
CP – Heat capacity parameters for pure liquid


Cp J  mol1  K 1  A  BT  CT 2  DT 3  ET 4
DIE0 – Coefficients for pure liquid dielectric const.
F
 E
T
MSE Databank: MSEPUB
Data items specifically used by MSE model
- In “Aqueous Phase” chapter
Other data items:
R_UQ, Q_UQ
UNIQUAC size (R) and surface (Q) parameters
well-defined group values (Reid et al. 1987)
SOLU (Two values are given)
solubility of a species (usually organic
component) in water and solubility of water in
organic.
MSE Databank: MSEPUB
Interactions pertaining to MSE model
– In “Interaction” chapter
• UNIQ – UNIQUAC parameters (primarily for
neutral-neutral interactions)
Q0IJ Q1IJ Q2IJ Q3IJ Q4IJ
Q0JI Q1JI Q2JI Q3JI Q4JI
aij  Q0 IJ  Q1IJ * T  Q 2 IJ * T 2  Q 3 IJ  Q4 IJ * T * xi x j
a ji  Q0JI  Q1JI * T  Q 2JI * T 2  Q 3JI  Q4JI * T * x j xi
aij  a ji
For most systems, Q3IJ, Q4IJ,
Q3JI, and Q4JI are set to zero
MSE Databank: MSEPUB
Interactions pertaining to MSE model
– In “Interaction” chapter
MIDRANGE – Middle-range parameters (primarily
for neutral-ion and ion-ion; can be used for
neutral-neutral)
BMD0 BMD1 BMD2 BMD3 BMD4
CMD0 CMD1 CMD2 CMD3 CMD4

Bij  bij  cij  exp I x  0.01

bij  BMD0  BMD1 * T  BMD2 / T  BMD3 * T 2  BMD4 * lnT
cij  CMD0  CMD1 * T  CMD2 / T  CMD3 * T 2  CMD4 * lnT
MSE Databank: MSEPUB
Interactions pertaining to MSE model
– In “Interaction” chapter
DENUNIQ – UNIQUAC density parameters
D0IJ D1IJ D2IJ
D0JI D1JI D2JI
aij
P
a ji
P
 D0 IJ  D1IJ * T  D 2 IJ * T 2
 D0JI  D1JI * T  D 2 JI * T 2
MSE Databank: MSEPUB
Interactions pertaining to MSE model
– In “Interaction” chapter
DENMID – Middle-range density parameters
DMD1 DMD2 DMD3 DMD4 DMD5
DMD6 DMD7 DMD8 DMD9 DMD0
Bij
( 0)
(1)


( 2)
 Bij  Bij * e xp  I X  0.01  Bij * P
P
( 0)
Bij  DMD1  DMD4 * T  DMD5 * T 2
(1)
Bij  DMD2  DMD3 * T  DMD6 * T 2
( 2)
Bij  DMD7  DMD8 * T  DMD9 * T 2  DMD0 / T
Regression Adjustable
Parameters
Excess Properties
• UNIQUAC parameters –
Q0IJ Q1IJ Q2IJ Q3IJ Q4IJ
Q0JI Q1JI Q2JI Q3JI Q4JI
• Middle-range parameters –
BMD0 BMD1 BMD2 BMD3 BMD4
CMD0 CMD1 CMD2 CMD3 CMD4
• UNIQUAC density parameters –
D0IJ D0JI D1IJ D1JI D2IJ D2JI
• Middle-range density parameters –
DMD1 DMD2 DMD3 DMD4 DMD5
DMD6 DMD7 DMD8 DMD9 DMD0
Regression Adjustable
Parameters
Standard state Gibbs energy and entropy
(appear in the databank as GREF and SREF)
•
•
•
•
•
•
GRFS – std. state Gibbs energy for solid
SRFS – std. state entropy for solid
GREF – std. state Gibbs energy for aqueous species
SREF – std. state entropy for aqueous species
GRFV – std. state Gibbs energy for vapor species
SRFV – std. state entropy for vapor species
Regression Adjustable
Parameters
Standard state heat capacities
• CPS1, CPS2, CPS3, CPS4, CPS5 – heat capacity
equation parameters for solid species
Cp  CPS1  CPS 2 * TK 
CPS 3
TK2
 CPS 4 * TK2  CPS 5 * TK3
HKF EOS parameters (aqueous species)
• HA1 HA2 HA3 HA4 (P dependency)
• HC1 HC2 HW (T dependency)
Regression Adjustable
Parameters
Coefficients for equilibrium constant K: A,
B, C, D can be adjusted as needed
B
2
log K  A 
 C * TK  D * TK
TK
OLI-MSE Data Regression
Steps
 Collecting relevant literature data
 Customizing chemistry model
 Create a private databank, if necessary, with
species of interest; create new species if not in DB
 Set up chemistry model using OLI/Express or
ESP Process, with the private databank
 Define variables using OLI internal variables, if
necessary, in the -.mod file
Create a Private Databank
 Changes can be made to a private
databank without affecting MSEPUB (the
public MSE databank)
 Parameters developed may be based on
proprietary data and are not going to be
in public domain
 How to create a private databank
Set up a chemistry model
 Change “current directory” to your working
directory
 Using OLI Express or OLI/ESP
 Include the private databank
 Select Mix-Solvent H3OION-based framework
 Define variables using OLI internal variables, if
necessary, in the -.mod file
List of Some Commonly Used
OLI Internal Variables
Variable name
Description
T
PT
PH
-IN
-AQ, -ION
H2O
L-AQ, L-ION
LH2O
-PPT, -.nH2O
YX-O
V
A-AQ, A-ION
AH2O
KDENMAS
temperature
pressure
pH
inflows
mole-frac in soln
mole-frac of H2O
ln (mole-frac in soln)
ln (mole-frac of H2O)
precipitates and hydrates
vapor mole-fractions
2nd liquid phase mole-frac
total vapor moles
ln (activity coef, x)
ln (activity coef. of H2O,x)
ln (equilibrium K-values)
density of solution
Default units
Kelvin
atmospheres
moles
moles
moles
g/L
Comparison of Variables in OLI/MSE
and OLI/Aqueous Framework
MSE
Aqueous
Concentration Units
mole-fraction; e.g.
SO4ION=x(SO4-2)
HSO4ION=x(HSO4-)
H2SO4AQ=x(H2SO4-aq)
H2O=x(H2O)
Concentration Units (V6.7 or older)
molality (mol/kg H2O); e.g.
SO4ION=m(SO4-2)
HSO4ION=m(HSO4-)
H2SO4AQ=m(H2SO4-aq)
H2O=55.5084 for all systems
Water activity
AH2O=ln γwater
Water activity
AH2O=ln awater
DEFINE AWATER=EXP(AH2O+LH2O)
DEFINE AWATER=EXP(AH2O)
where LH2O=ln(xwater)
Comparison of Variables in OLI/MSE
and OLI/Aqueous Framework
MSE
Aqueous
Activity coefficients
AKION=ln γK+x,∞
γK+m,∞= xw•γK+x,∞
Activity coefficients
AKION=ln γK+m,∞
Mean activity coefficient:
Mean activity coefficient:
DEFINE GAMMA=
EXP(LH2O+(AKION+ACLION)/2.0)
DEFINE GAMMA=
EXP((AKION+ACLION)/2.0)
Based on (for 1:1 electrolyte):
ln ±,m= ½ • (ln K+,m+ ln Cl-,m)
Comparison of Variables in OLI/MSE
and OLI/Aqueous Framework
MSE
Aqueous
Equilibirum Constant
KMXAQ=ln KMX∞,x
Equilibirum Constant
KMXAQ=ln KMX∞,m
, x , x

x
x
X
K , x  M X  M
, x
x MX
 MX
, m , m

m
m
X
K , m  M X  M
, m
m MX
 MX
log K , m  log K , x  n  log55.509
where ∆n is the change in number of moles in reaction
(∆n=1 for MXAQ=MION+XION).
OLI-MSE Data Regression
Steps
Collecting relevant literature data
Customizing chemistry model
Preparing regression input file
Regression Input
Input file (-.inr) structure:
$TITLE
A line containing characters to explain the file
$CONTROL
Has several options
$PARAMETERS
The heart of the regression
$DATA SET X
Has a global parameter section and data section;
An input file can have a number of data sets.
Regression Input File (-.inr)
$TITLE
A line containing characters to explain the file
$CONTROL
Options are:
MAXIT xx
(Maximum number of iterations, default= 50)
QFIT x.x (Convergence tolerance, default= 1.0E-05)
METH x
(Regression method)
0 - Brown’s algorithm, Uses MARQ parm
1 - Strict Decent (default)
2 – Semi Strict Decent, Uses MARQ and SCALING)
MARQ x.x (Marquardt scaling parm – METH=1 or 2 default=1.0)
SCALING x.x (Factor for adjusting MARQ – Meth=2 default=1.5)
NUMERICAL
(Forces numerical derivative calculation)
TRACE
(Produce ElectroChem output at every iteration)
OBJECTIVE x (Change Objective function)
1 - (calc value/exp value – 1) default
2 – (max(calc or exp value)/min(calc or exp value) – 1)
3 – (calc value – exp value)
ERROR xxxxx (Error assign to non-converged points, default=0)
CSV variable-list (specify variables to be printed for each datum in a CSV file)
Regression Input File (-.inr)
$PARAMETERS
The heart of the regression
Format:
P01 1.0 1.023E-2 -1
1.
KION CLION
species1
Alias
species2
Initial value
Active=1.0
Not active=0.0
BMD0
Lower and upper bound
(not used, only for place holding)
regression
parameter
Regression Input File (-.inr)
$PARAMETERS
P01 1.0 1.023E-2
………
-1
1.
KION CLION
BMD0
P05 1.0 -45035.5
P06 1.0 38.35
-1
-1
1.
1.
NAACETPPT
NAACETPPT
GRFS
SRFS
species
Alias
Initial value
Active=1.0
Not active=0.0
Lower and upper bound
(not used, only for place holding)
regression
parameter
Consistency in standard state properties:
Using ELEM in input file
Values of ∆Gf0 (GREF), ∆Hf0 (HREF),
and S0 (SREF) are related by
H f 0   G f 0  T  S f 0
S f 0  S 0   S 0elem
This is done using an ELEM statement in input file —
Consistency in standard state properties:
Using ELEM in input file
Example: if ∆Gf0 and S0 for NAACETPPT (solid sodium
acetate) are adjusted in regression,
In input file (at the end of $PARAMETERS section):
ELEM NAACETPPT 1.0 12.26 2.0 1.372 1.0 49.0 1.5 31.21
The formation process and the standard state entropy for
each of the elements are
Na(s) + 2 C(s) + O2(g) + 1.5 H2(g) = CH3COONa (s)
12.26 1.372 49.0
31.21 (in cal/mol.K)
Consistent values of ∆Gf0, ∆Hf0, S0 for NAACETPPT
Consistency in standard state properties:
Using ELEM in input file
Example: NH2CO2ION (carbamate ion)
In input file, write:
ELEM NH2CO2ION 1.0 1.372 0.5 45.77 1.0 49.005 1.5 31.21
The formation reaction of carbamate ion and the standard
state entropies are:
C(s) + 0.5 N2(g) + O2(g) + 1.5 H2(g) = NH2CO2-(aq) + H+(aq)
1.372
45.77
49.005
31.21
0.0
Consistent values of ∆Gf0, ∆Hf0 and S0 for NH2CO2ION
Regression Input File (-.inr)
$DATA SET X
Global parameter section
TEMPERATURE
100.0
These lines may be
PRESSURE
1.2249
eliminated if values of
H2OIN
0.965
variables are given in
METHANOLIN
0.035
data section
FREE PT
PT allowed to be adjusted
FIX V 1.0E-9
# of FREE variables = # of FIX variables
SC_INDEX list of solids
allow calculations under super-saturation
Data section
independent variables
dependent variables
DATA T METHANOLIN H2OIN : PT YMETHANOL
100 0.035 0.965 1.2249 0.191
100 0.074 0.926 1.4085 0.313
100 0.163 0.837 1.7419 0.496
……………
Example: NaCl-H2O
Define variables at the end of -.mod file:
……..
EQUATIONS
DEFINE AW=EXP(AH2O+LH2O)
DEFINE PHI=-(AH2O+LH2O)*H2OIN/(2.0*NACLIN)
DEFINE DENGCC=0.001*DENMAS
END
lnaw  ln w  ln xw
Translation of the 1st
and 2nd DEFINE:
xw

ln a w
2  x NaCl
Examples – in c:\MSE-Reg
Systems
1.
2.
3.
4.
5.
6.
7.
8.
9.
NaCl+H2O
Methanol+H2O
Methanol+H2O+NaCl
Sulfamic acid+H2O
Phenol+H2O
Benzene+H2O
Benzene+H2O+NaCl
MethaneSulfonic Acid+H2O
AlCl3+HCl+H2O,
AlCl3+NaCl+H2O
10. ZnCl2+HCl+H2O
11. Zn(NO3)2+HNO3+H2O
File Names
NaCl.inr
Methanol.inr
MWNaCl.inr
NH3SO3.inr
Phenol.inr
Benzene.inr
BzNaCl.inr
MSA.inr
AlCl3.inr
ZnHCl.inr
ZnHNO3.inr
Example: NaCl-H2O
Set up input file: NACL.INR
$DATA SET 1
SC_INDEX H2OPPT NACLPPT NACL.2H2O
DATA T PT H2OIN NACLIN : PHI AW CP DENGCC
variables need to be defined
……….
$DATA SET 4
SC_INDEX H2OPPT NACLPPT NACL.2H2O
DATA T PT H2OIN NACLIN H2OIN NACLIN : HDILUT
heat of dilution
initial x
final x
(cal/mol)
This is the fixed format for heat of dilution
Example: NaCl-H2O
Two ways to use solubility data in regression:
Saturation concentration Scaling tendency as
as dependent variables:
dependent variables:
$DATA SET 10
FREE NACLIN
FIX NACLPPT 1.0E-9
SC_INDEX ALL NACLPPT
DATA T PT H2OIN : NACLIN
25.0 1.0 0.90021 0.09979
50.0 1.0 0.89812 0.10188
.........
$DATA SET 9
SC_INDEX ALL
DATA T PT H2OIN NACLIN : SC_NACLPPT
25.0 1.0 0.90021 0.09979 1.0
50.0 1.0 0.89812 0.10188 1.0
………..
Scaling tendency (SC_solid = IAP/Ksp)
must be 1.0 at saturation
Heat of Mixing (DHMIX):
MeOH-H2O and MeOH+H2O+NaCl
Methanol+H2O (methanol.inr)
DATA T PT METHANOLIN H2OIN METHANOLIN H2OIN METHANOLIN H2OIN : DHMIX
25 1
25 1
1
1
0
0
0
0
1
1
0.25
0.3
0.75
0.7
………..
soln 1 (x)
soln 2 (x)
final mix. (x)
-210.28
-213.96
∆Hmix
(cal/mol)
Methanol+H2O+NaCl (MWNaCl.inr)
DATA
T PT METHANOLIN H2OIN NACLIN METHANOLIN H2OIN NACLIN METHANOLIN H2OIN NACLIN : DHMIX
12.5 1
1
0
0
0
0.9969 0.0031
0.2
0.7975 0.0025 -215.225
12.5 1
1
0
0
0
0.9969 0.0031
0.25
0.7477 0.0023 -226.004
∆Hmix
…………
soln 1 (x)
soln 2 (x)
final mix. (x)
– The order of components in each of the 3 solutions must be the same
(cal/mol)
Example: Methanol + NaCl + H2O
Define variables at the end of MWNaCl.mod file:
……..
DEFINE GTRNA=8.3147*T*(ANAION+LOG(32.0424/18.0152)+LOG(0.997/0.7866))
DEFINE GTRCL=8.3147*T*(ACLION+LOG(32.0424/18.0152)+LOG(0.997/0.7866))
DEFINE GTRE=GTRNA+GTRCL
END
Based on
 w 
0

 tr G NaCl w  M   2 RT ln

 M 


 MM 

,
x

,
x

 RT ln
 ln
  2 RT ln
 M 

Na  , M
Cl  , M 
 w 
Example: Phenol-H2O
Set up chemistry model: phenol.mod
Define variables at the end of phenol.mod file:
……..
EQUATIONS
DEFINE PKPA=PT*101.325
END
Example: Phenol-H2O
Using LLE data in regression:
• Activity ratio as dependent variables
DATA T PT C6H5OHIN H2OIN C6H5OHIN H2OIN : LLE_C6H5OHAQ LLE_H2O
25 1 0.0173
0.9827
0.3223
0.6777
1
1
29.6 1 0.0153
0.9847
0.316
0.684
1
1
…….....
equil. x in 1st liq phase equil. x in 2nd liq phase
LLE_C6H5OHAQ=aC6H5OHAQ(1st)/aC6H5OHAQ(2nd)
LLE_H2O=aH2O(1st)/aH2O(2nd)
must be 1.0 at LLE
Example: Phenol-H2O
Using LLE data in regression:
• Equilibrium concentrations as dependent variables
DATA T PT H2OIN C6H5OHIN : C6H5OHAQ H2O XC6H5OHAQO XH2OO
25
1
4.88928 1.0
0.0173
0.9827 0.3223
0.6777
29.6 1
5.03682 1.0
0.0153
0.9847 0.316
0.684
…….....
initial moles
equil. x in
equil. x in
in mixture
aqueous phase
organic phase
Other LLE cases:
Benzene.inr
BzNaCl.inr
Other Example: AlCl3.inr
Solubility of AlOOH as a function of pH:
$DATA SET 1
SC_INDEX ALL ALOOHPPT
H2OIN 55.509
FREE PT
FIX V 1.0E-12
FREE HCLIN
FIX PH 2.731
FREE ALOOHIN
FIX ALOOHPPT 1.0E-12
DATA T NACLIN PH : ALOOHIN
152.4 0.1
2.614
6.442E-06 ; 2001PBW g-AlOOH
152.4 0.1
2.731
3.707E-06 ; 2001PBW g-AlOOH
…………
Other Example: MSA.inr
Using additional constraint on invariant points for
solubility data regression
…….
$DATA SET 2
SC_INDEX ALL
DATA T PT H2OIN CH4SO3IN : SC_H2OPPT SC_CH4SO3.3H2O WEIGHT
-75 1.0 0.8360 0.164
1.0
1.0
5.0
$DATA SET 3
SC_INDEX ALL
DATA T PT H2OIN CH4SO3IN : SC_CH4SO3.3H2O SC_CH4SO3.1H2O WEIGHT
-54.5 1.0 0.685
0.315
1.0
1.0
5.0
$DATA SET 4
SC_INDEX ALL
DATA T PT H2OIN CH4SO3IN : SC_CH4SO3.1H2O SC_CH4SO3PPT WEIGHT
-15 1.0 0.220
0.780
1.0
1.0
5.0
Constrains in regression parameters
General Format: Pnn=Pmm x y
Example:
Let
$PARAMETERS
P01 1 0.1
-1.
P02 1 0.001
-1.
P03 0 0.
-1.
P04 0 0.
-1.
P05 1. 32.
-1.
P06 1. -40000. -1
P07 0 0.
-1.
P08 1. -46000. -1
P03=P01
P04=P02 2.5
P07=P05 1.0 10.0
Pnn=x*Pmm+y
P03=P01
P04=2.5*P02
P07=P05+10.0
1.
1.
1.
1.
1.
1.
1.
1.
SPE1 SPE2 BMD0
SPE1 SPE2 BMD1
SPE3 SPE4 BMD0
SPE3 SPE4 BMD1
SPE5PPT SRFS
SPE5PPT GRFS
SPE5.H2O SRFS
SPE5.H2O GRFS
Examples:
ZnHCl.inr
ZnHNO3.inr
OLI-MSE Data Regression
Steps
Collecting relevant literature data
Customizing chemistry model
Preparing regression input file
Running the regression
Running the regression using
REGRESS.EXE
• Open a DOS window
• Change to the working directory (e.g. C:\MSE-Reg)
Your private databank (if any), input file (inr), model file
(dbs) must be in the working directory
• Run REGRESS (e.g. located in C:\OLI70\SYS):
C:\MSE-Reg>C:\OLI70\SYS\REGRESS nacl nacl
model inr
name name
OLI-MSE Data Regression
Steps
Collecting relevant literature data
Customizing chemistry model
Preparing regression input file
Running the regression
Reviewing the regression output
Regression Output
Files to review:
OUE
CSV – overwritten by results from the next iteration
NRM – overwritten by results from the next iteration
Files to review:
OUE –
– Summary of input data
– Summary of results for each iteration
• Parameters
• comparison of cal- and exp- values
• Overall NORM (=∑(cal-exp)2) and NORM for each data set
– Complete results from the final iteration:
•
•
•
•
Equilibrium concentrations in the vapor and liquid phases
Activity coefficients of all aqueous species
Fugacity coefficients of all vapor species
Equilibrium constants for all associated species
Files to review:
CSV – Lists information at every single data point;
Good for making plots
– Deviations for all dependent variables, as defined by
OBJECTIVE (in $CONTROL section)
– Comparisons for the calculated and measured values
for all dependent variables
– Values of independent variables as input
– Convergency flag (0=converged, 1=not converged)
– Phase indicator (e.g. “L1 V”, “L1 L2”, “L1 V S”)
– All other variables listed in INR file under
$CONTROL section with CSV statement
Files to review:
NRM –
– Regression parameters
– Point-by-point comparison of caland exp- values for all dependent
variables
– All other parameters used (but
not adjusted) in the calculations
Part of the
OUE file: