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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