Flash flow simulation for a oil, gas and water composite fluid in non-equilibrium and steady state

Nonisothermal Multiphase Flow in Pipelines under Nonequilibrium Conditions

Guillermo Michel and Faruk Civan

Michel, G., Modeling of Multiphase Flow in Wells under Nonisothermal and Nonequilibrium Conditions , M.S. Thesis, November 2007, University of OklahomaMichel, G., Civan, F., Modeling Nonisothermal Rapid Multiphase Flow in Wells under Nonequilibrium Conditions, SPE Production and Operations Journal, May 2008Michel, G., Civan, F., Modeling Rapid Multiphase Flow in Wells and Pipelines under Nonequilibrium and Nonisothermal Conditions, SPE 107958, presented at the 2007 Rocky Mountain Oil & Gas Technology Symposium, Denver, Colorado,16-18 April 2007Michel, G., Civan, F., Modeling Nonisothermal Rapid Multiphase Flow in Wells under Nonequilibrium Conditions, SPE 102231, presented at the 2006 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 2427 September 2006.

OutlineDescription of the ProblemTransport Phenomena in Producing WellsThe non-equilibrium conditionEstimating the relaxation in gas phase separation Predicting the liquid hold up with correlationsPredicting the liquid hold up with a slip ratio formulationApplicationPressure gradientTemperature gradientDryness gradientRelaxation TimeSummaryWhat is the problem of interest?

The difference in the Velocity of the Phases indicates the occurrence of slippageThe Heat Dissipation causes a drop in TemperatureThe Fluid Expansion causes a change in TemperatureHow can it be modeled?The reservoir fluid is considered as a multiphase systemA Homogeneous Area-averaged Model is adoptedThe infinitesimal element for the model is the cross-sectional areaThe system properties are defined as the average over a cross-sectional area.

Homogenous Area-Averaged Model

Mass ConservationMomentum ConservationEnergy Conservation

Constant cross-sectional areaNo gain or loss of massHomogeneous Model at Steady-State

MassMomentumEnergy

Unknown variables : density, velocity, pressure and temperatureA fourth equation is needed to give closure to the system All remaining properties are estimated from correlations7The Nonequilibrium Condition

The slippage of the liquids is caused by the buoyancy of gas bubbles and gravitational pull exerted to the liquid dropletsThis result in a higher mobility of the gas phase which tends to travel faster than the liquid phase The slippage of the liquids causes a difference in velocities at which the phases are flowingMixture properties can not be calculated by using the formulations for ideal mixturesThe Nonequilibrium ConditionMixture VelocityMixture Density

Volumetric Fraction of the liquid phases

The following inequalities applies to the non-equilibrium conditionVolumetric Fraction of the gas phase

Relaxation Time of Gas Phase Separation

The law of mass conservation for the gas phase is applied to the previously defined model for attaining its closure.The mass transfer from the liquids to the gas is not assumed instantaneouslyThe mass generation of the gas phase is estimated by considering a relaxation in the time for the gas phase separation from the liquidsRelaxation Time of Gas Phase Separation

The quality or dryness at equilibrium conditions is obtain by phases are flowing at the same velocityThe relaxation in time can be characterized for reservoir fluids flowing at steady-stateA constitutive equation defines the mixture density in order to estimate the pressure gradientThis constitutive equation is applied to the previously defined model for attaining its closure.Liquid Holdup Modeling

The mixture density is estimated by averaging using the volumetric fractions of the gas phase (void fraction) and the liquid phases (liquid holdup)The mixture velocity is set equal to the volumetric flux even though the flow is at non-equilibrium conditions.Liquid Holdup ModelingThe most intuitive parameters in the dimensional analysis are the fractional flow of the gas phase and the liquids.The non-slip density of the mixture is calculated by using the fractional flow of the phasesThe superficial velocity of the phases, the density of the phases, the liquid superficial tension, the pipe diameter and the gravitational force are the most common parameters used in the dimensionless analysis of the liquid hold up prediction

Predicting the Liquid HoldupVarious correlations over dimensionless parameters were developed for identifying the flow-pattern of the phasesThis flow-patterns are usually classified as: bubble, slug, annular and mist flowEach flow-pattern uses a specific correlation for predicting the liquid holdupThe prediction of the liquid holdup is discontinuous when a change in flow-pattern occurs

BubbleSlugAnnularMistSlip Ratio Formulations

It is desired to utilize a parameter capable of characterizing the density, velocity and liquid holdup of the mixture simultaneouslyThe slip ratio proves to be a parameter with such capability

The slip ratio is defined as the ratio of the actual velocity of the gas phase to the actual velocity of the liquid phasesThe liquid hold up is expressed in terms of the slip ratioThe void fraction is expressed in terms of the liquid hold upSlip Ratio Formulations

The quality or dryness of the mixture is directly related to the slip ratioThe mixture density formulation can be rearranged to be related to the slip ratioThe mixture velocity formulation can be rearranged to be similarly relatedNote that if the value of the slip ratio is equal to the unit then the flow is at equilibrium

Proposed Liquid Holdup Model

This value has to be estimated or measuredThe slip ratio is estimated by a quadratic interpolation where the non-slip density of the mixture is the independent variableThe mixture is considered at equilibrium when the mixture is either a saturated gas or liquidThe mixture density is equal to the density of the saturated phasenProposed Liquid Holdup ModelAdvantagesThe need of correlations for liquid holdup prediction is avoidedThe prediction is continuous in the saturated/under-saturated transitionsThe prediction is continuous for all transitions of flow type

DisadvantagesThe slip ratio at the inlet needs to be measured or estimated.It was only tested for oil wells : Bubble and Slug flow.Pressure Gradient Two-phase Flow of Light Oil

Pressure Gradient Two-phase Flow of Heavy Oil

Pressure Gradient Three-phase Flow of Heavy Oil

Temperature Gradient Two-phase Flow of Light Oil

Temperature Gradient Two-phase Flow of Heavy Oil

Temperature Gradient Three-phase Flow of Heavy Oil

Dryness Gradient and Relaxation Time Two-phase Flow of Light Oil

Dryness Gradient and Relaxation Time Two-phase Flow of Heavy Oil

Dryness Gradient and Relaxation Time Three-phase Flow of Heavy Oil

SummaryThe proposed approach predicts a continuously varying liquid-holdup by interpolating the slip ratio.The heat dissipation to the surroundings ,and fluid expansion, and energy loss by friction cause a non-linear temperature drop.The upward motion of reservoir fluids in producing wells can be successfully modeled by the developed homogenous model which has been closured with the proposed model for liquid holdup prediction.The relaxation time of gas separation proved to be an adequate property for characterizing the deviation form the equilibrium for reservoir fluids.The homogenous area-averaged model can be closured using the conservation law for the gas phase and the relaxation time of gas separation from the liquid phases.