Flash Computation and EoS Modelling for Compositional Thermal Simulation of Flow in Porous Media

215 Pages·2019·6.937 MB·English

by  Duncan Paterson

Springer Theses
Recognizing Outstanding Ph.D. Research
Duncan Paterson
Flash Computation
and EoS Modelling
for Compositional
Thermal Simulation
of Flow in Porous
Media
Springer Theses
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Duncan Paterson
Flash Computation and EoS
Modelling for Compositional
Thermal Simulation of Flow
in Porous Media
Doctoral Thesis accepted by
Technical University of Denmark, Kongens
Lyngby, Denmark
123
Author Supervisors
Dr. Duncan Paterson Assoc. Prof. Wei Yan
Department ofChemistry Department ofChemistry
Technical University of Denmark Technical University of Denmark
Kongens Lyngby,Denmark Kongens Lyngby,Denmark
Prof. Erling H.Stenby
Department ofChemistry
Technical University of Denmark
Kongens Lyngby,Denmark
Prof. Michael L.Michelsen
Department ofChemical Engineering
Technical University of Denmark
Kongens Lyngby,Denmark
ISSN 2190-5053 ISSN 2190-5061 (electronic)
SpringerTheses
ISBN978-3-030-11786-3 ISBN978-3-030-11787-0 (eBook)
https://doi.org/10.1007/978-3-030-11787-0
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’
Supervisor s Foreword
Phase equilibrium is a common phenomenon and often one of the determining
factors in describing and designing processes of industrial importance, such as
explorationanddevelopmentofpetroleumreservoirs,oilandgastransport,carbon
dioxide capture and sequestration, and various separation processes. In the simu-
lationoftheseprocesses,thecomponentdistributionacrossphasesisusuallysolved
by flash computation, with its most common form being the two-phase isothermal
flash. As a module repeatedly used in the process simulator, flash computation is
expected to be both robust and efficient.
In the modern process simulation, there is an increasing demand to handle
systemswithmorecomplexphaseequilibria.Thecomplexitycanarisemainlyfrom
two somewhat related aspects: high non-ideality that requires advanced thermo-
dynamic models and multiple phase equilibrium that is often a result of the high
non-ideality. Consequently, it is necessary to develop simulators that can incor-
poratemodelsmorecomplicatedthantheclassicalcubicequationsofstateandcan
perform multiphase flash without a significant compromise in robustness and effi-
ciency. There are also other complicating factors for the phase equilibrium calcu-
lation in simulation, for instance, other flash specifications like isenthalpic flash,
and phase equilibrium with simultaneous chemical reactions.
ThisPh.D.thesiscoversawiderangeoftopicsfrommodelingtoalgorithmand
simulation in the area of thermal recovery of heavy oil. In particular, it provides
some generic calculation algorithms for complex phase equilibrium. Heavy oil
productionbysteaminjectionconsumestremendousenergyandwater.Byaddition
ofsolvent,theuseofenergyandwater,aswellasthegreenhousegasemission,can
be reduced dramatically. This new recovery method also results in a highly
non-ideal multiphase system and a challenging compositional simulation problem.
Apparently, the study in this thesis is directly beneficial to people working on
thermal recovery. However, its significance is not limited to this narrow area. The
most valuable contribution by the author is the generic algorithms for multiphase
flash using different specifications, some even allowing chemical reaction equi-
librium. The algorithms are applicable to simulation of numerous processes other
than thermal recovery.
v
vi Supervisor’sForeword
Besides an effective solution for multiphaseisenthalpic flashunder theclassical
framework, the thesis presents a new flash calculation framework for multiphase
systems that can handle phase equilibrium and chemical reaction equilibrium
simultaneously. The framework is particularly suited for systems with many
phases and reactions. The thesis also shows how the new framework can be
generalized for different flash specifications and different independent variables.
Dr. Christos Tsanas in our group has recently applied the new framework to a
variety of important chemical and phase equilibrium problems covering reactive
distillation, production of biodiesel and geochemical reactions with electrolytes.
Iexpectthatthisthesiscaninspiremoreresearcherstodevelopbetteralgorithmsfor
phase equilibrium calculation of complex systems in the simulation of various
processes.
Kongens Lyngby, Denmark Assoc. Prof. Wei Yan
November 2018
Abstract
Theproductionofheavyoilisgraduallybecomingmoreviable,asboththepriceof
productiondecreasesandthepriceofoil(overthelongterm)increase.Thereserves
ofheavyoilarefargreaterthantheexistingreservesofconventionaloil;however,
itisoftennoteconomicallydesirabletoextract.Heavyoilischaracterisedasavery
viscousanddensesubstance,whichflowsveryslowlyundergravityatatmospheric
temperature. As such, it is often necessary to use steam to reduce the viscosity
of the oil to enhance production. Novel production enhancement techniques can
utilise a light hydrocarbon solvent to further increase recovery. The simulation
ofthesereservoirsisnottrivial,andduringproduction,theyundergolargechanges
in temperature and pressure depending upon the production strategy used.
Furthermore, the use of a light hydrocarbon solventcan lead to highly asymmetric
mixtures and the appearance of a second oleic phase. However, an accurate sim-
ulation is necessary due to the high cost of the production and the requirement for
reliable predictions for new production enhancement strategies. In this work, the
thermodynamic models used to represent the fluid and the methods of flash cal-
culation suitablefor multiphase mixtures are studied. The finalaim isto develop a
reservoir simulator incorporating some of these elements.
Toaccuratelyrepresentthefluidphasesinequilibriuminaheavyoilreservoir,it
isnecessarytouseanequationofstate(EoS).Thereareahugenumberofpossible
equations of state (EoS’s) available. In this work, a number of these models are
comparedforheavyoil-relatedbinarysystemstoevaluatewhicharebestsuited.The
accuracyofeachmodeliscompared,anditisfoundthatiftheinteractionbetween
the water and hydrocarbon phases is not considered to be important, then the
commonly used cubic EoS’s with the van der Waals mixing rules are suitable
(optimally using two binary interaction parameters). If more complex interactions
areconsideredimportanttothesimulation,thenthecubicEoS’scanbeusedwiththe
Huron–Vidal-type mixingrules (usingthenon-random two-liquid (NRTL) activity
coefficientmodel).ThemorecomplexEoS’ssuchascubicplusassociation(CPA)or
PC-SAFTcan also be usedand are generally asaccurateas theHuron–Vidal type.
vii
viii Abstract
Anotherissueassociatedwiththermalsimulationisthatitisnecessarytoaddan
energybalancetothesystemofPDEsused.Itiscommontousethetemperatureas
anadditionalprimaryvariable.Theresultingisothermalflashspecificationcanlead
tosome problemsduringtransient simulation.Thefluidinsomeofthegridblocks
may become narrow boiling. The enthalpy of a narrow boiling mixture changes
rapidly due to very small changes in the temperature or pressure. This can lead to
issues with convergence and potential oscillations during Newton steps. A related
issueiswhenthesolutionrequiresmorephasesthancomponentstomeettheenergy
balance equation, and this cannot be solved when using isothermal flash. This can
oftenoccur closetosteam injection wells(wherecomponentsotherthanwatercan
be stripped away). An approach using the energy directly in the flash calculation
(e.g. isobaric and isenthalpic flash) is explored in this work and an algorithm
presented which takes only slightly more computational resources than the con-
ventionallyusedisothermalflash.Thisisdemonstratedtoberobustforanumberof
mixtures, and an approach tailored for the flash calculation of mixtures containing
water is described.
The issue of multiple coexisting equilibrium phases is also examined. The
conventional isothermal flash framework is complex and cumbersome when deal-
ing with more than two or three phases. A new method (modified RAND) is
presented based on the related chemical equilibrium problem. This method is pri-
marily examined for multiphase isothermal flash, with a robust implementation
described. An extension to other state function-based flash specifications is
developed using the new proposed framework. Furthermore, the conventional
methodofsolvinganEoSataspecifiedtemperatureandpressureisabandonedand
a method which co-solves the EoS with the equilibrium equations is described
(vol-RAND). A different approach to solving state function-based flash specifica-
tions is also considered, where the EoS is solved at the given state function vari-
ables resulting in a minimisation without nonlinear constraints. This proposed
approach has not yet been tested.
A thermal, EoS-based reservoir simulator is developed from an isothermal
simulator. The energy balance partial differential equation is added, and the tem-
perature is used as an additional primary variable. The EoS’s compared for heavy
oil-related fluids are implemented in the simulator. A multiphase flash algorithm
using modified RAND and stability analysis skipping is added to the simulator.
Finally, a test case is used to demonstrate that some of the more complex EoS
modelscanbeusedandthemultiphaseflashalgorithmissuitable.Withthethermal
reservoir simulation tool developed, it is possible to carry out further comparisons
and add more complexity in future work.
Preface
Throughmyacademicstudiesandworkingasaprocessengineer,Irepeatedlyused
processsimulatorstoaidinthedesignofindustrialequipment.Attheheartofthese
simulators(similartooilreservoirsimulators)arethermodynamicmodelsandphase
equilibrium calculations. Unfortunately, there are often significant limitations in
these simulators (e.g. which thermodynamic model to select; ability to model
non-isothermalproblems;abilitytomodelmultiphaseproblems;andtheirabilityto
include chemical reactions). Contributing to solving these problems first attracted
me to carrying out this research.
Thisworkisparticularlyapplicabletoheavyoilproductionsimulation;however,
much of the work (particularly Chap. 4) is of importance to general process and
reservoir simulation. Production from heavy oil reservoirs typically uses steam to
enhance production. This leads to high levels of emissions and is often economi-
callyunviable.Onegoalofthisworkistoaidthosedevelopingreservoirsimulators
to deal with the complex problems involved inthermalsimulationin the hope that
new,improvedtechniquescanaidincheaperandmoreenvironmentallyfriendlyoil
production.
As a first step, it is necessary to check whether current models are suitable for
these complex problems and find what are their respective weaknesses and
strengths. Simple models may not be accurate enough; however, there are a huge
array of more complex models, each boasting their own advantages. This can lead
to confusion as to which is actually best suited to each problem. In this work, we
tried to carry out an unbiased comparison (in Chap. 2) to find the advantages of a
range of models for heavy oil-related systems. I hope that this is of use to those
involvedinsuchsimulationsasaguidetowhatwillbemodelledaccuratelybytheir
chosen model and what may not.
The main contributions of the work in Chaps. 3 and 4 are focused on dealing
with complex phase equilibrium calculations. The algorithms used for these cal-
culations are generally based on the seminal work of Michelsen (1982a, b). As a
supervisor to this project, he contributed a great deal to the development of the
RANDmodelspresentedinthiswork.Onedifficultyinpresentingnewmethodsfor
phase equilibrium calculations is that they are at the heart of the simulators and
ix