PHASE-SPLITTING PREDICTION IN ISOTHERMAL FLASH CALCULATIONS By Alejandro Antonio

316 Pages·2010·13.58 MB·English

PHASE-SPLITTING PREDICTION IN ISOTHERMAL FLASH
CALCULATIONS
By
Alejandro Antonio Romero
B.A.Sc. (Chemical Engineering) Universidad Nacional Autonoma de Mexico
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF APPLIED SCIENCE
in
THE FACULTY OF GRADUATE STUDIES
CHEMICAL ENGINEERING
We accept this thesis as conforming
to the required standard
THE UNIVERSITY OF BRITISH COLUMBIA
July 1989
© Alejandro Antonio Romero, 1989
In presenting this thesis in partial fulfilment of the requirements for an advanced
degree at the University of British Columbia, I agree that the Library shall make it
freely available for reference and study. I further agree that permission for extensive
copying of this thesis for scholarly purposes may be granted by the head of my
department or by his or her representatives. It is understood that copying or
publication of this thesis for financial gain shall not be allowed without my written
permission.
Department of Chl*iic*l t=r$\nte.f\*3
The University of British Columbia
Vancouver, Canada
Date Ju/jf Zt,lW
DE-6 (2/88)
Abstract
The development of processes that operate at conditions where multiple fluid-phase equi
libria may occur demands fast and reliable simulation algorithms. The success of these
algorithms depends on the correct prediction of the number and compositions of the
phases present at a given temperature, pressure and overall fluid composition. The most
commonly used routine for this purpose is the isothermal (single-stage) flash calculation.
A robust and efficient method to predict phase-splitting previous to performing an
isothermal flash is implemented in this work. It is based on the thermodynamic stability
analysis of the source phase using a Gibbs energy tangent-plane criterion. Depending on
the outcome of the phase-split tests, the system may be declared stable as a single phase
and thus no further calculations are needed, or unstable in which case a potential two- or
three-phase solution can be obtained. Only in this last instance would the corresponding
flash calculation follow, depending on the nature and quantity of the phases found: a
vapour-liquid (VL) or a liquid- liquid (LL) flash if two phases are predicted, or a multi
phase flash (VLL) when three phases are expected.
In addition to readily recognizing the number and type of phases present, the sta
bility tests provide excellent initial composition estimates for the flash which assure fast
convergence to the stable solution. Even though the algorithms developed can be used
with any suitable model to calculate equilibrium properties, cubic equations of state are
used throughout in this work as a single model to describe all fluid phases.
n
Table of Contents
Abstract ii
List of Tables vi
List of Figures viii
List of Symbols xi
Acknowledgement xv
1 Introduction 1
1.1 Purpose and scope 2
1.1.1 The flash algorithms 3
1.1.2 Thermodynamic models 3
1.2 Structure of this study 4
2 Previous works on phase-splitting 6
2.1 Thermodynamic stability 6
2.2 Phase-splitting 12
2.2.1 Liquid-liquid split tests 12
2.2.2 Gibbs energy minimization algorithms 18
2.2.3 Mass balance approaches 30
3 Proposed algorithm 35
3.1 General scheme 36
iii
3.2 Phase search strategy 43
3.2.1 Vapour phase search 49
3.2.2 Liquid phases search 57
3.3 Initialization procedures 67
3.3.1 Vapour phase 67
3.3.2 Liquid phases 68
3.4 Phase removal tests 78
3.4.1 Multiphase flash method 81
3.4.2 Bubble- and dew-point equations method 84
3.4.3 Coupled method 88
4 Results and discussion 90
4.1 Systems tested 91
4.2 Phase search initialization 97
4.2.1 Vapour phase 97
4.2.2 Liquid phases 99
4.3 Phase search performance 107
4.3.1 Vapour phase 110
4.3.2 Liquid phases 115
4.3.3 Wegstein's method 128
4.4 Phase removal tests 135
4.4.1 Multiphase flash method 135
4.4.2 Coupled method 138
4.4.3 Bubble- and dew-point equations method 139
4.5 Overall phase-splitting prediction performance 142
IV
5 Conclusions and recommendations 152
5.1 General conclusions 152
5.2 Specific remarks and recommendations 153
Bibliography 158
Appendices 163
A Two- and three-phase flash algorithms 163
A.l Isothermal VL or LL flash 163
A.1.1 Limit for the phase ratios 167
A.1.2 VL flash initialization 168
A. 1.3 LL flash initialization 168
A.2 Isothermal VLL flash 170
A.2.1 Limit for the phase ratios 174
A.2.2 V LL flash initialization 175
A. 3 Wegstein's method 175
B Activity coefficient models in the phase-splitting algorithm 178
B. l Activities and standard states 179
B.2 Vapour and liquid phases search 181
B.3 Liquid phase initialization 182
Appendices 185
C Description and listings of the computer programs 185
v
List of Tables
4.1 Initial composition estimates for the vapour phase search using Raoult's
law and for the flash calculation using the incipient vapour found 98
4.2 Composition estimates for the incipient liquid phases obtained with the
various initialization methods tried, composition of the incipient phases
found and equilibrium values for two feed compositions in System 4- • • • 100
4.3 Comparison of the reliability and efficiency of the four methods tested to
provide initial compositions for the liquid phase search 103
4.4 % RMS deviation of the incipient phase estimates and of the equilibrium
values from the actual incipient phases composition (mole fraction) in the
prediction of LL immiscibility for System 1 105
4.5 Vapour and liquid phases search performance for System 2 from 90 to 320
K indicating the stable solution, the number of iterations required for con
vergence and the CPU time (in milliseconds) required for the initialization
plus the phase search 109
4.6 Phase equilibria predictions comparison for System 5 when the phase-
splitting algorithm is used with the optional additional phase search to find
a missed vapour giving correct VL equilibria solutions 112
4.7 Equilibria predictions when the phase-splitting algorithm is used with and
without the optional additional phase search to find a missed liquid yielding
correct LL equilibria solutions for System 4 120
vi
4.8 Performance of Wegstein's method in the vapour and liquid phase search
as a function of parameters w and t for Systems 1, 2 and 3 compared
max
to the use of direct substitution 130
4.9 Performance of the phase removal tests and of the subsequent flash calcula
tion in the phase-splitting prediction for Systems 1, 2 and 3 near saturation
point conditions 137
4.10 Comparison of the phase removal tests reliability with and without the
additional phase search versus the direct three-phase flash calculation for
Systems 1 and 6 140
4.11 Comparison of the prediction of the phase distribution for System 1 at
different temperatures with the direct three-phase flash calculation and with
the phase-splitting algorithm proposed followed by the corresponding type
of flash. 144
4.12 Predictions of the equilibrium conditions for System 2 at different tem
peratures with the direct three-phase flash calculation and with the phase-
splitting algorithm proposed followed by the corresponding type of flash. . 146
4.13 Number and type of phases predicted for System 3 at different pressures
with the direct three-phase flash calculation and with the phase-splitting
algorithm proposed followed by the corresponding flash 148
4.14 Equilibria predictions for System 7 at three temperature and pressure con
ditions with the direct three-phase flash calculation and with the phase-
splitting algorithm proposed followed by the corresponding flash 150
4.15 Summary of the phase equilibrium predictions for the seven systems tested
obtained with the direct three-phase flash calculation and with the phase-
splitting algorithm proposed followed by the corresponding type of flash
when required 151
vn
List of Figures
2.1 Molar Gibbs energy of mixing at constant temperature and pressure for a
binary liquid system presenting a miscibility gap 9
2.2 Thermodynamic stability regions for a binary liquid mixture at constant
pressure showing the connodal and spinodal domes 10
2.3 Vapour-liquid thermodynamic stability regions in a Gibbs energy as a func
tion of composition diagram for the methane- propane system at 278 K and
33.6 bar (modified from Radzyminski and Whiting) 11
2.4 Graphical representation of Michelsen's stability test for the case of a stable
binary system 27
2.5 Michelsen's stability test and initial guess compositions for an unstable
binary system 28
3.6 Flow chart of the phase-splitting algorithm proposed in this work 40
3.7 Erroneous prediction of VL equilibrium due to bypass of a liquid incipient
phase when using Michelsen's method for the n-hexane-water system at
378 K and 4-08 atm (diagram modified from Heidemann) 45
3.8 Bypass of a vapour incipient phase when using the tangent plane criterion
leading to an incorrect LL equilibrium prediction in a hypothetical binary
mixture 45
3.9 Additional phase search to find the n-hexane rich liquid incipient phase for
the n-hexane-water system (378 K and 4-08 atm) leading to the correct
prediction of LL equilibria 46
viii
3.10 Detection of an incipient vapour phase by means of the additional search
proposed for the binary mixture of Figure 3.8 leading to the proper predic
tion of a VL stable system 47
3.11 Binary system stable as VL for which two incipient liquid phases are found
in the phase search, one being superfluous 80
4.12 Gibbs energy of mixing diagram for the n-hexane- water system at 378 K
and 5 atm (System 4) showing that both components are immiscible almost
throughout the entire composition range 101
4.13 Gibbs energy of mixing diagram for the hydrogen sulphide-methane system
at 190 K and 38 atm (System 5) for which the vapour phase is detected
with the additional phase search leading to the correct prediction of VL
equilibria 113
4.14 Gibbs energy of mixing as a function of composition for the methane-n-
butane-water system (System 6) at 311 K and 60 atm considered as a
vapour 123
4.15 Gibbs energy of mixing surface for System 6 considered as a liquid in the
entire composition range at 311 K and 60 atm 123
4.16 Gibbs energy of mixing for the stable system (System 6 at 311 K and 60
atm) obtained by superimposing the vapour and liquid-like surfaces and
retaining the least Gibbs energy values at every composition 124
4.17 Gibbs energy of mixing as a function of composition for the methane-
carbon dioxide-hydrogen sulphide system (System 1) at 171 K and 20 atm
corresponding to the stable solution 126
4.18 Contour lines of the Gibbs energy of mixing surface for System 1 as a
stable system 126
ix