A CFD Approach to the displacement of
oil by injection of water in
Hele-Shaw Cell
Authors: G. C. Mariano, R. A. F. Machado and M. B. Quadri
Federal University of Santa Catarina – UFSC
Chemical Engeneering Department (EQA)
Control Process Laboratory (LCP)
Hele-Shaw Cell
Bibliographical revision
�� StudyStudy toto immiscibleimmiscible flowsflows
-- MainMain propertiesproperties::
Interface Interface tensiontension
AdhesivenessAdhesivenessAdhesivenessAdhesiveness
CapillarityCapillarity
ViscosityViscosity,, densitydensity..
Picture Picture TreatmentTreatment
Experimental Estudy
Experimental Estudy
�� ConditionsConditions ofof thethe representedrepresented betterbetter problemproblem::
1 - Distance between plates is 11,,11mm,mm, 4545°°;;
2 - InterfaceInterface accommodates to 3535 cmcm (h(h)),, volumetricsvolumetrics fractionsfractions assit to
a function step;
Material Material andand MethodsMethods
Computational Study
3 - Initial conditions the interface is plane with angle in the contact
with the walls ((100100 ee 135135°°));;
4 - It considered adhesivinessadhesiviness inin thethe wallswalls;;
5 - Considered fluidsfluids waterwater andand soysoy oiloil;;
6 - IncompressibleIncompressible fluidsfluids at temperature to 2525°°CC;;
7 - ProfileProfile pressurepressure hydrostatichydrostatic;;
8 - LaminarLaminar flowflow..
��Definitions the mesh: Definitions the mesh:
-- 268340268340 elementselements HexahedralHexahedral;;
-- CentralCentral part,part, where the draining of
Material Material andand MethodsMethods
Computational Study
-- CentralCentral part,part, where the draining ofthe interface occurs, presentsgreatergreater refinerefine ofof thethe meshmesh;;
-- EspaceEspace between plate presentspresentsrefinerefine ofof 1010 characteticcharactetic elementselementsrepresentingrepresenting 33DD for Hele-Shaw cell.
MathematicalMathematical modellingmodelling
�� The moment conservation equation (NavierThe moment conservation equation (Navier--Stokes):Stokes):
Computational Study
Where,
ρ is density (imcompressible fluid)
G is gravity
μ is viscosity
P is pressure.
MathematicalMathematical modellingmodelling
�� TheThe HagenHagen--PoiseuillePoiseuille equationequation::
Computational Study
Where,
h is the distance among plates
µ is viscosity
Ф displacement potential.
ComputationalComputational resultsresults
Two simulations with laminarlaminar flowflow in identical conditions(“time step” 0,01) present two differentdifferent solutionssolutions;; it is verifiedan residualresidual andand randomrandom parallelparallel processingprocessing errorerror (clusterPVM).
Computational Study
AdjustAdjust ofof thethe ““timetime stepstep”” and determination this step thatthatrepresentsrepresents thethe smallsmall errorerror..
ComputationalComputational resultsresults
Computational Study
VerificationVerification thethe repeatabilityrepeatability ofof aa computationalcomputational simulationsimulationapplying a smaller interface tension (0,100 N/m).
ComputationalComputational resultsresults
Computational Study
ComputationalComputational resultsresults
Simulation wichwich lagerlager reductionreduction ofof interface interface tensiontension..
Computational Study
ComputationalComputational resultsresults
Verifying of adhesivenessadhesiveness in in thethe wallwall. .
Computational Study
ComputationalComputational resultsresults
SimilaritySimilarity in the simulated interface pattern.interface pattern.
Computational Study
ComputationalComputational resultsresults
OilOil areaarea in in delaydelay (experimental).(experimental).
Computational Study
ComputationalComputational resultsresults
OilOil areaarea in in dealydealy ((computationalcomputational). ).
Computational Study
Conclusion
� The HeleHele--ShawShaw cellcell becomes possible to relate densitydensity,,viscosityviscosity,, interfaceinterface tensiontension wichwich thethe processprocess toto injectinject waterwaterforfor displacementdisplacement anan oiloil phasephase;;
� The modelmodel can be considered a valuablevaluable tooltool,, it wasshow capablecapable toto describedescribe thethe waterwater//oiloil pumpingpumping inin HeleHele--ShawShaw cellcell,, presentingpresenting wealthwealth ofof detailsdetails,, allowingallowing toto testtest thethesensibilitysensibility ofof physicalphysical andand operationaloperational parametersparameters..
Bibliographical reference
BAPTISTA, R. M.; QUADRI, M. B.; MACHADO, R. A. F.; BOLZAN, A.; NOGUEIRA, A.
L.; MARIANO, G. C.; LOPES, T. J., Effective Interfacial Tension and Geometrical
Parameters Relationship for the Description of Oil Leakages from Submarine
Pipelines. 8º International Conference on Chemical & Process Engineering.
Napolis, Milano : AIDIC Servizi S.r.I, V. 11, P. 401-406, 2007.
BENTSEN, R.G., The physical origin of interfacial coupling in two-phase flow through
porous media. Transport Porous Media, vol. 44, p.109-122, 1987.
BRACKBILL, J.U., KOTHE, D.B., ZEMACH, C., A Continuum Method for Modeling
Surface Tension. Journal of Computacional Physics, vol. 100, p. 335-354, 1992.
MARIANO, G. C.; CARDOSO, F.F.; LOPES, T. J.; NOGUEIRA, A. L.; BAPTISTA, R. M.;
QUADRI, M. G. N.; MACHADO, R. A. F.; QUADRI, M. B., Um Estudo
Experimental sobre a Instabilidade da Interface no Deslocamento de Óleo por
Injeção de Água. Petro & Quimica, v. 299, p. 1-8, 2007.
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