Vapour Liquid EquilibriumAdrian C ToddHeriot-Watt UniversityDEPARTMENT OF PETROLEUM ENGINEERING

Importance of Vapour Liquid EquilibriumMultiphase aspects of hydrocarbon mixtures important part of reservoir management.

Reservoir flow & well productivity, facility design and pipeline transport.Predicting relative amounts of phases and their physical properties is an important part.Behaviour of multicomponent mixtures in reservoirs and their production to surface is a serious challenge.

Total Production System

Complexity of allocation of produced oil to supply fieldsMain issues to reservoir engineer.Multiphase behaviour-rel.perm etcVolumes between reservoir and surface.Physical properties of gas and oil in reservoir and at surface

Vapour-liquid equilibriumPhase diagram defines area bounded by bubble point and dew point curves where two phases exist.Too simple to describe as involatile oil and solution gas.

Vapour-liquid equilibriumThroughout the production process from the reservoir through the separator to the stock tank conditions, large volumes of gas are generated from the reservoir oil.The oil shrinks.

Volume factors can be determined directly in the laboratory or from equilibrium calculations

Vapour-liquid equilibriumBesides separator calculations vapour liquid equilbrium calculations used for.

Reservoir calculations Two phase pipeline flow calculations Process calculations

Vapour-liquid equilibrium calculationsThe grid block of a simulator can be considered to be the separator of a process unit.

A simplified reservoir simulation model

KEY FEATURES

- a grid block structure

- each block has a set of

uniform properties

(but kx ky kz)

Vapour-liquid equilibrium,VLE, calculationsVLE calculations have been restricted to separate areas; reservoirs and wells, surface operations, pipelines, onshore treatment and refinery operationsIncreasing trend is the integration of this to determine for example impact of a change in a reservoir parameter on refinery or pipeline outputs.

Ideal solutionsRaoultsLawDaltons Law

Ideal Equilibrium RatioEquilibrium ratio is the ratio of the composition in the vapour phase to that of the liquid phase.From Raoults and Daltons Laws

Equilibrium RatioKj defined at a particular pressure and temperatureOther names: K-factors, K values, equilibrium vapour liquid distribution coefficients

Non Ideal SystemsIdeal solution assumptions cannot be applied to multicomponent hydrocarbon fluids in reservoir flow, transport and processing.Ideal assumptions only apply to low pressures and moderate temperatures.Different methods have been developed for VLE for non ideal systems.Equilibrium ratio concept from ideal systems are applied to provide non ideal K values.Non ideal K values are obtained experimentally, from empirical charts or from EOS.

Vapour Liquid Equilibrium CalculationsThe calculations for determining amount of liquid and vapour phases and their respective properties concentrations are important in reservoir calculations as well as within a separator.In a grid block of a reservoir simulator we need to know amounts of gas & liquid, which impact on relative permeabilities. The compositions impact on density and viscosity which are all part of the flow calculations.

Vapour Liquid Equilibrium CalculationsVLE equations used in a process separator calculations are the same as used in a compositional reservoir simulator.

Vapour Liquid Equilibrium Equations

Vapour Liquid Equilibrium Equationsm = the number of components

Vapour Liquid Equilibrium Equations

Vapour Liquid Equilibrium EquationsSimilarlyBy multiplying by V we get

Vapour Liquid Equilibrium EquationsMethod of calculation

1. Select Kj for each component at the T&P of the system.

2. Assume a vapour-liquid split such that V+L=1

3. Calculate either V,L,Sxj or Syj

4. Either (i) check V&L calculated against assumed V or Lor (ii) determine if Sxj or Syj =1.0

5. Repeat the calculation until assumed value correct or Sxj or Syj =1.0

In a simulator these calculations take place at each grid block

Dew Point Pressure CalculationDew point where first drop of liquid condenses.The composition of the drop of liquid is higher in heavier component.Composition of vapour is same as system

At dew pointIterate on Pd selecting Kj till equation =1

Bubble Point Pressure CalculationBubble point where first bubble of gas appears.The composition of the bubble of gas is higher in lighter components.Composition of liquid is same as system

At bubble pointIterate on Pb selecting Kj till equation =1

Separator ProblemsUsing VLE equations the various production volumes and black oil parameters can be obtained.GOROil formation volume factor

Separator ProblemsThe operating conditions of the separator impact on the values of GOR and Bo.

Example of Separator Problem (McCain)Calculate the GOR , stock tank gravity and Bo which will result from a two stage separation of the following mixture. Use separator conditions of 76oF and 100psig. The mixture is a liquid at its bubble point of 2,695 psig and 220oF

Example of Separator Problem (McCain)Step 1 Calculate composition of separator gas & Liquid

Example of Separator Problem (McCain)V=0.4291 and L =0.5709Compositions:

Example of Separator Problem (McCain)Calculate compositions of stock tank liquid.Feed to stock tank is liquid from separator

Example of Separator Problem (McCain)Vst =0.1351 and Lst= 0.8649Compositions >

Integration of Black-Oil and Compositional ApproachThe problem has illustrated the combination of a compositional based prediction of phase volumes and associated properties and that based on the black-oil model, parameters:oil formation volume factor and GOR.This combination overcomes the weaknesses of the simple two component black-oil model.The big issue is the values for K.