Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Measurement and Modelling of Absorption of Carbon Dioxide
into Methyldiethanolamine Solutions at High Pressures
Ph.D Dissertation
Even Solbraa
14.February 2003
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
What has been done ?
• A high pressure experimental equipment has been built and new
high pressure experimental data are presented
• Equilibrium and kinetic limitations related to CO2 removal at high
pressures in MDEA solutions are identified
• NeqSim - a general simulation program for natural gas processing
operations has been developed. It is based on equilibrium and
non-equilibrium models developed in this work. Many types of
processes can now be solved effectively using a general nonequilibrium two-fluid model
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
How are the results used today?
• Capacity and kinetic limits of high pressure absorption
processes of CO2 in MDEA-solutions are estimated
• The simulation program developed is used to solve and teach
thermodynamics and mass transfer processes
• High pressure equilibrium (e.g. dew point) and non-equilibrium
(e.g. drying) processes are solved in an effective way
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Outline
1. Introduction to Natural Gas Processing and Transport
2. Equilibrium and Non-Equilibrium Model Development
3. Presentation of the Simulation Program Developed
4. Modelling and Regression to Experimental Data
5. Experimental Work and Results
6. Conclusions
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Natural Gas Processing
Lean Amine
Natural Gas
Natural Gas + CO2
Rich Amine
CO2 Gas
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Sweet Gas
Lean Amine
Solution
Random and structured
packings:
Film Flow
Acid Natural Gas
Rich Amine
Solution
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
CO2 removal with physical and chemical solvents
Physical Solvent
(water):
PCO2
CO2
Water+CO2
Chemical Solvent
(MDEA):
CO2
MDEA
Water
CO2
CO32HCO3-
xCO2
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Two Illustrative and Case Studies
1. Almost all models developed are
low pressure models (GE-models).
Problem to reach design specification
in high pressure (100 bar) CO2
absorption plant operating at 70-80°C
using MDEA
Condensation of Liquid Water in
Sub Sea Dry Gas Pipeline
operating between 100-200 bar
2. High pressure equilibrium and mass
transfer data not available
1. Erroneous predictions of water
dew-point with standard equations
of state in high pressure natural gas
systems
2. Non-equilibrium models for
two-phase pipe flow not available
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Outline
1. Introduction to Natural Gas Processing and Transport
2. Equilibrium and Non-Equilibrium Model Development
3. Presentation of the Simulation Program Developed
4. Modelling and Regression to Experimental Data
5. Experimental Work and Results
6. Conclusions
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
The Non-Equilibrium Two Fluid Model
The Non-Equilibrium Two Fluid Model
Closure Relations
Thermodynamic Models
Mass Transfer / Kinetic Models
Physical Property Models
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Weak Electrolyte Calculation Procedure
MDEA  H 2O  CO 2
HCO3  MDEA
Reactive/Non-reactive TP-flash algorithm
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Thermodynamic Modelling of Amine Solutions
State of the Art
Polynoms
(Kent and Eisenberg, 1976)
+ Easy and fast
- Too simple, no physics
Electrolyte GE-models
Future
+ Relatively easy and fast
Austgen (1989), Li and Mather (1994) - Problematic to add
supercritical components
- Low pressure model
Electrolyte Equations of State + Generally applicable
Furst and Renon (1993), this work
- Computational demanding
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Thermodynamic Models
Year
Type of Fluid
Non-Polar
Polar
Electrolyte Polymers
1950
DebyeEoS-Models GE-Models Huckel
1980
EoS-Models EoS-Models GE-Models Empirical
models
1990
2000
Empirical
models
EoS-Models EoS-Models EoS-Models other
EoS-Models EoS-Models EoS-Models EoS-Models
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Definition and Calculation of Thermodynamic Equilibrium
Equation of States
xii P  yii P
Parameters:
• Critical Temperature and Pressure
• Accentric Factor
GE-models
xi  i Psat ,i
 vi  P  Psat ,i  
  yii P
 e xp 


RT


Molecular Parameters:
• Vapour Pressure of Pure Components
• Molar Volumes in solution
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Development of Two New Electrolyte Equations of State
General Equation
of State
 Ar T ,V , n  
nRT
P   
 
V
V

T , P
The Modelling
Procedure
Contributions to the
Helmholtz Energy
 A  A0

 RT
Find
  A
A0  Best A  A0
  
  
Molecular
RT
RT
 
 RF  EoS

 A  A0

 
 SR1  RT
0
Electrolyte
Find Best

 A  A0
A A

  
 
Terms
RT
 SR 2 
 LR  RT


 BORN
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Development of Two New Electrolyte Equations of State
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Equations of State Considered
Equations of State
Mixing Rules
• RK
(Redlich Kwong, 1949)
• no
• SRK
(Soave, 1971)
• Classic
(Van der Waals, 1905)
• PR
(Peng and Robinson, 1979)
• Huron Vidal
(Huron-Vidal, 1979)
• ScRK (Scwartzentruber and Renon, 1989) • Wong-Sandler
• CPA
(Kontegorgios, 1999)
Electrolyte Extensions
• Debye-Huckel (Debye-Huckel, 1952)
• MSA (Blum and Høye, 1982)
• Furst and Renon (Furst and Renon, 1993)
(Wong and Sandler, 1993)
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Molecular Terms of Electrolyte Equations of State
Absolute average relative deviation1) [%] between experimental and calculated vapour pressures and
densities with different equation of states
Component
RK SRK PR ScRK2) CPA3)
Experimental Data
Methane
Perry (1998),
vapour pressure:
15.6
2.8
2.8
Borgnakke et. al (1997)
0.9
liquid density:
6.5
8.1
6.5
5.8
gas density:
17.7
3.9
4.6
1.5
Nitrogen
Perry (1998),
vapour pressure:
10.1
1.7
2.2
Borgnakke et. al (1997)
0.5
liquid density:
4.5
4.2
4.5
4.1
gas density:
11.8
3.3
3.8
2.3
CO2
Perry (1998),
vapour pressure:
21.4
0.3
0.8
2.2
Borgnakke et. al (1997)
0.2
liquid density:
14.9 11.6 4.0
11.5
1.9
gas density:
24.9
3.2
2.5
3.5
1.9
MDEA
Noll et.al. (1998)
vapour pressure: >>100 83.3 67.2
5.1
4.2
liquid density:
20.8 13.3 3.16
14.4
1.1
gas density:
Water
Perry (1998),
vapour pressure: >>100 11.5 6.9
1.2
Borgnakke et. al (1997)
0.3
liquid density:
30.7 27.8 18.8
27.8
1.1
gas density:
>>100 15.5 10.6
5.9
1.7
1)
Deviation (%) = 100 x (experimental-calculated)/experimental
2)
The polar coefficients in the ScRK-EOS coefficients were fitted for water, CO2 and MDEA
3)
The coefficients in the CPA-EOS were fitted to experimental data
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Mixing Rules for Molecular Terms
Absolute average deviations (%) between experimental data and different models for the calculation of
solubility of gasses in water and water in gas.
Gas
Number of Fitted
Parameters
Nitrogen
nitrogen in water
water in nitrogen
CO2
CO2 in water
water in CO2
Methane
methane in water
water in methane
No.points
used for
fitting1)
SRK +
classic
SRKHV2)
ScRKHV
PRHV
SRKWS
CPA +
classic
1
4
4
4
5
1
13
78
>>100
32.2
3.0
8.1
7.1
17.6
4.3
10.0
8.7
11.6
29.7
28.2
43
57
>>100
45.0
6.0
13.5
6.1
10.6
5.8
11.8
7.6
15.4
12.0
22.5
176
215
>>100
52.2
6.4
13.1
5.5
10.6
5.9
10.1
7.6
10.4
31.8
14.1
1) See chapter 8 for references to the actual experimental data used in the fitting
2) The  parameter in the Huron Vidal and Wong Sandler mixing rule was not fitted
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Electrolyte Terms
 A  A0 
nk nW
l kl

  
k
l V 1   3 
 RT SR 2
 A A0

 RT

 LR





4
 LR
2
n i Z i2 
 1  
i

i
 A  A0 
Ne2  1  ni Zi2

  1  *


 RT  BORN 4 0 RT  Ds  i  i
Osmotic coefficients of salt solutions calculated using the electrolyte ScRK-EOS
 3V
3N
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Evaluation of Electrolyte Terms
Evaluation of different electrolyte models for the calculation osmotic coefficient and mean ionic coefficient
for 28 halide salt solutions1)
Model
Electrolyte
ScRK-EOS
Electrolyte
CPA-EOS
1)
No. of
experimental
points used in
fitting
230
230
Osmotic
coefficient
abs.avg.rel.dev
[%]
2.1
Mean ionic
activity
abs.avg.rel.dev
[%]
5.5
2.3
4.9
Experimental
data
Robinson
(1952)
Robinson
(1952)
Salt concentrations: 0.1-6.0 molal. Salt solutions: NH4Cl, LiCl, LiBr, LiI, NaCl, NaBr, NaI, KCl, KBr, KI,
KBr, KI, RbCl, RbBr, RbI, CsCl, CsBr, CsI, MgCl 2, MgBr2, MgI2, CaCl2, CaBr2, MgI2, CaCl2, CaBr2, CaI2,
SrCl2, SrBr2, SrI2, BaCl2, BaBr2, BaI2
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Predictions With the Electrolyte Model
Density of Ionic Solution
Calculated and experimental density of an aqueous NaCl solution
Mean Ionic Activity Coefficient
Calculation of mean ionic activity coefficients of salt solutions using the electrolyte ScRKEOS.
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Non-Equilibrium Modelling
Scientific Work
Simulation Tools Software
1900:
Fick’s law for diffusion
1920:
Fourier law of heat transfer
1950:
Kinetic Theory of Gasses
1970:
Multicomponent Mass Transfer
1980:
Non-Equilibrium Thermodynamics Stage Efficiencies
1990:
Molecular Simulation
2000:
Resistance at Interface
This work
Equilibrium Models
OLGA
HYSYS
Fick’s law
Simple
Simple Maxwell
Maxwell Stefan
Stefan
General
General Maxwell
Maxwell Stefan
Stefan
ASPEN PLUS
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Generalized Maxwell Stefan Equations
Multicomponent Maxwell
Stefan Equation:
 J   ct  B   d 
1
+ General model
n
xi
x
Bii 
 k
Din k 1 Dik
i  `k
 1
1 
Bij   xi 

i  j and i, j  1,
n 1
- 2,...,
Relatively
 Dij Din 


complicated
- Need thermodynamic model
Generalized Driving Force:
n


ct RTdk  c k T , P k  k  k  P  k  Fk    j Fj 
j 1


Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
The Enhancement Factor
CO2
MDEA  H 2O  CO 2
Water
yCO2
CO2
yCO2
xCO2
xCO2
Ei 
J i ,reactive
J i ,non reactive
HCO3  MDEA
Water
MDEA
CO2
HCO3MDEA+
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Calculation of the Enhancement Factor
Two Ways to Estimate the Enhancement Factor:
• Analytical Expressions
(for simple reactions, e.g reversible first order reactions)
• Numerical Solutions of Film
(for coupled and reversible reactions)
This work:
analytical
ECO2 
k  MDEA D

1
2t
CO2 ,eff
kCO2 ,eff 2
*
 J   ct ( E ) k *   xCO ,i  xCO
,b 
2
*
xCO
2 ,b
2
CO2 fraction at chemical equilibrium in liquid bulk
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
The Generalized Non-Equilibrium Two Fluid Model
• Conservation of total mass
• Conservation of components
• Conservation of momentum
• Conservation of energy
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Outline
1. Introduction to Natural Gas Processing and Transport
2. Equilibrium and Non-Equilibrium Model Development
3. Presentation of the Simulation Program Developed
4. Modelling and Regression to Experimental Data
5. Experimental Work and Results
6. Conclusions
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
NeqSim – a General Non-Equilibrium Simulator
• General modelling tool for non-equilibrium and equilibrium processes
• Based on rigorous thermodynamic models
• Fluid mechanics based the on the one- or two fluid model
• Implemented in an object oriented language
(Java/Python object oriented design where everything is an object)
• Suitable for being used as a modelling tool
(general parameter fitting routines implemented)
• Validated against experimental data (equilibrium/non-equilibrium)
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
NeqSim – a General Non-Equilibrium Simulator
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
NeqSim - Examples of use
• Multiphase flash calculation
• Construction of phase envelopes
• Weak electrolyte calculations
• Process plant simulation
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Parameter Fitting Routines
Shi-Square Fitting
 yi  y  xi ; a  
2
 (a)   

i
i 1 

N
2
Minimized using the LevenbergMarquardt Method
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Outline
1. Introduction to Natural Gas Processing and Transport
2. Equilibrium and Non-Equilibrium Model Development
3. Presentation of the Simulation Program Developed
4. Modelling and Regression to Experimental Data
5. Experimental Work and Results
6. Conclusions
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Thermodynamic Properties of Mixtures
ScRK-EOS + Huron Vidal
Mutual solubility of Water+CO2:
Freezing points of MDEA+Water:
CPA-EOS + Classic
Mutual solubility of Water+CO2:
Mutual solubility of Methane+Water:
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Solubility of CO2 in water+MDEA solutions
Ref.
MDEA (wt%)
Temperature (K)
Electrolyte
ScRK-EoS
Jou
et.al.wt
(1993)
20.5
%
35 :
MDEA
Number
of points
313, 373
Loading range
(mol CO2/mol
amine)
0.005-0.795
35
50 wt% MDEA
AAD
(%)
26.5
Jou et.al. (1982)
23.4
48.9
298,313,343,373,393
298,313,343,373,393
0.0009-1.833
0.0001-1.381
54
55
29.6
28.4
Austgen et.al.
(1991)
23.4
48.9
313
313
0.006-0.842
0.04-0.671
9
5
21.0
21.0
Chakma and
Meisen (1987)
19.8, 48.9
373
0.04-1.304
17
18.8
Bahiri (1984)
20.0
311, 339
0.157-1.336
44
12.8
Kuranov (1996)
18.8-19.2
32.1
313, 333, 373, 393
313, 333, 373, 393
0.209-1.316
0.195-1.157
33
34
16.3
23.2
Rho et.al. (1997)
5.0
20.5
323, 348, 373
323, 348, 373
0.03-0.684
0.026-0.847
19
31
16.4
11.3
Mac Gregor and
Mather (1991)
23.4
313
0.124-1.203
5
31.4
Average
Deviation
26%
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
High pressure solubility of CO2 and methane in water+MDEA solutions
Electrolyte ScRK-EoS
Estimated bubble point pressure
30 wt % MDEA
Estimated PCO2:
30 wt% MDEA
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
High pressure solubility of methane in CO2+water+MDEA solutions
Electrolyte ScRK-EoS
Estimated methane solubility
30 wt % MDEA
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Capacity Loss of Amine Solution at 100 bar and 70C
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Outline
1. Introduction to Natural Gas Processing and Transport
2. Equilibrium and Non-Equilibrium Model Development
3. Presentation of the Simulation Program Developed
4. Modelling and Regression to Experimental Data
5. Experimental Work and Results
6. Conclusions
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
The High-Pressure Wetted Wall Column
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Experiments Done in This Work
Experiment
Type
Water-CO2nitrogen
Water-CO2nitrogen
MDEAwater-CO2nitrogen
Number of Comments Temperature Pressure Purpose
Experiments
[bar]
[C]
12
Low pressure 25, 40
20
Study physical
experiments
mass transfer –
compare to
exciting low
pressure data
35
High
25, 40
50,
Measure new
pressure
100,150 high pressure
experiments
data
48
High
25, 40
50,
High pressure
pressure
100,150 absorption data
experiments
of CO2 in
MDEA
solutions
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Experimental Results – Reference Data CO2 +Water
1/ 3
 kL    2 
*
kL      
D  g 
Reference
 K  Re a Sc b
Reynolds Number K
Yih et.al. (1982) 300<Re<1600
This work
230<Re<1750
2.99510-2
3.10110-2
a
b
Abs.rel.dev.
[%]
0.2134 0.50 13.0
0.2201 0.50 10.5
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Experimental Results – Reference Data CO2, MDEA and water
ECO2  1 
 k  MDEA D
2t
CO2 ,eff
kCO2 ,eff
2
 E 1
1 
k2t  k2tT 313 K  exp  a  

 R  T 313K  
k2t T 313.15 K   6.45 m3 / kmol s
Ea  50.0 kJ
mol
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Conclusions
 A high pressure wetted wall column was designed and constructed
 New mass transfer data were obtained for absorption of CO2 into MDEA-solutions at
pressures between 50 and 150 bar
 An electrolyte EOS (electrolyte ScRK-EOS) was used to model the thermodynamics
of the CO2-MDEA-water systems
 The electrolyte EOS was able to represent the experimental data for the systems CH4CO2-MDEA-water with good accuracy
 A general non-equilibrium mass transfer model was developed
 A non-equilibrium simulator – NeqSim – was implemented in a Java code
 Examples of how to do non-equilibrium process simulations were presented
 The non-equilibrium model developed is able to represent the experimental mass
transfer data of this work with a good precision.
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Conclusions
 For a given partial pressure CO2, the capacity of MDEA solutions is lowered at
increasing pressures. The capacity can be reduced up to 40% at 200 bar total pressure
(inert gas methane)
 For a specified natural gas, the capacity of MDEA solutions will increase with
increasing gas stream pressures. This increase is not as high as we would expect from
only consideration of the increased partial pressure of CO2
 The reaction kinetics is not considerable affected by the total pressure (up to 150 bar
with nitrogen as inert gas)
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Case 1: Problem to reach design
specification inCase
high2:pressure
(100 bar)
CO2 Water
Condensation
of Liquid
absorption plant
operating
at Gas
70-80°C
usingoperating
in Sub
Sea Dry
Pipeline
MDEA
between 100-200 bar
Case 1:
Operation Chart 100 bar, 70-80C
12.0
Hysys
Operationline
10.0
Ideal Electrolyte EOS
Real Electrolyte EOS
CO2 Partial Pressure
8.0
6.0
4.0
2.0
0.0
0
0.2
0.4
0.6
Loading
0.8
1
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Case 2:
Solubility of water in methane:
Case 2: Condensation of Liquid Water
in Sub Sea Dry Gas Pipeline operating
between 100-200 bar
Equilibrium and Non-Equilibrium
Thermodynamics of Natural Gas Processing
Thanks
• Institute for Energy- and Process Technology
• Statoil
• Norwegian Research Council