Equilibrium Ratio Prediction and Equilibrium Ratio Prediction and CalculationCalculation

Adrian C Todd

Heriot-Watt UniversityHeriot-Watt University

DEPARTMENT OF PETROLEUM ENGINEERING

Heriot-Watt UniversityHeriot-Watt University

DEPARTMENT OF PETROLEUM ENGINEERING

Introduction

Previous section we introduced the concept of vapour-liquid equilibrium and its application in predicting multicomponent behaviour with respect to reservoirs.

In this section we will review the methods used to determine K values, which are at the foundation of VLE prediction methods.

Introduction

Compared to process facility calculations in petroleum engineering detailed definition of the composition of the fluid is not available.

Some of these undefined components may have significant impact on VLE behaviour.

The fluid in a reservoir is unique from its composition perspective.

Process versus reservoir compositional modelling

Process Engineering

Calculations for a single unit or a few in series.

Full compositional data is available.

Calculations to predict detailed compositional outcome.

Reservoir Engineering

Calculations part of a multi-grid block simulation. Hundred or thousand of process units.

Limited compositional data.

Calculations to predict phase volumes and physical properties.

Petroleum Engineering Vapour Liquid Equilibrium Challenge

Prediction of properties based on limited data

Applicable to multi-component mixtures

Accurate at predicting thermodynamic and volumetric properties over a wide range of pressures and temperatures and around and beyond critical point.

Be able to use pure component or binary mixture data which is available from literature or generated.

Importance of Critical PointImportance of Critical Point Critical point is unique condition where liquid and

vapour phases are defined.

Has therefore theoretical as well as practical significance.

In hydrocarbon processing knowledge of critical condition important since many of operations are near to the critical condition.

Behaviour near the critical point difficult test of prediction methods.

Equilibrium Ratio, K

Empirical methods

Based on Thermodynamic principles

Equilibrium Ratio, K

A range of approaches

Black Oil System.

Two components, stock tank oil & solution gas.

Experimental Data through K values.

Methods based on Equations of State

Experimental Data through K values

In a reservoir the distribution of components is not just a function of T & P but also influenced by composition.

Reservoir fluids are unique in composition.

No one has tested this fluid before!!

Compositional Model

Reservoir fluid

Gas at surface conditions

Oil at surface conditions

Distribution of compounds a

function of pressure,

temperature and composition

Empirical K values

Oil industry has relied on experimentally determined K values where K is plotted versus pressure for a constant temperature.

The K values are generated from specific compositions.

The challenge is to determine which K values are appropriate to our specific mixture.

At high pressure the K values are a function of T, P and composition.

The compositional influence is of great significance.

Pure component K values from one mixrure cannot be accurately applied to another

jj

j

yK

x

Empirical K values

The K values converge to unity at different pressures.This is called the convergence pressure

Empirical K values-Convergence pressure The K values converge to unity at different

pressures.

This is called the convergence pressure

K values at particular P&T are different.

Convergence pressure is a measure of the composition of the mixture.

Empirical K values-Convergence pressureK Value for a binary system

Empirical K values-Convergence pressureK Value for a light oil at 200oF

Empirical K values-Convergence pressure

Comprehensive set of K value data provided by NGPSA

Presented as a function of convergence pressure.

Challenge is to select convergence pressure for new fluid.

Empirical K values-NGPSA

Calculating Convergence Pressure How do we select convergence pressure which is

applicable to our fluid ?

Trial and error method.

Procedure is to convert the mixture into an equivalent two component mixture, usually based on methane and a heavier component.

Heavy component selected according to the composition of the non methane components and the weight fraction weighted critical properties.

Calculating Convergence Pressure Procedure Step 1 - Assume liquid composition

Step 2 - Identify the lightest component > 0.1mole%.

Step 3 - Calculate weight average critical properties to identify an equivalent component to define the binary.

Step 4 - Trace the critical locus of the binary.

Step 5 - Read the convergence pressure at the temperature of the desired ‘flash’ calculations.

Step 6 - Using K values for indicated convergence pressure carry out VLE, flash calculations to generate new liquid composition.

Step 7 Repeat steps 2 to 6 until assumed calculated convergence pressure is the same as calculated.

Convergence pressure for hydrocarbons

Convergence pressure for various oils.

Convergence Pressure Procedure ExampleThe gas-liquid equilibrium of a high shrinkage oil has been calculated.

The composition of the liquid formed at 75oF and 100psia is given.

A convergence pressure of 2000psia was used.

What value of the convergence pressure

should be used ?

Convergence Pressure Procedure Example

Composition of the liquid expressed as weight fraction

Convergence Pressure Procedure Example

Weight fraction excluding methane and calculated weight average critical properties

Equation of State Based Equilibrium Calculations

Equations of state can be used for the following purposes.

Representing PVT data to assist smoothing and improving interpolations

Prediction of vapour-liquid equilibria of mixtures.

Prediction of gas phase properties of pure fluids and their mixtures using minimum experimental data

Most favoured EOS

Peng Robinson & Soave, Redlich Kwong.

Equation of State Based Equilibrium Calculations

It is important to note that these calculations take place within each grid block in the finite element based compositional reservoir simulator.

They use therefore considerable computer load.

Equation of State Based Equilibrium Calculations - Procedure

Determine K values using quick method. e.g.Wilson equation

Determine phase volumes etc using VLE equations.

Solve cubic EOS written in terms of Z.

Three roots lowest -liquid highest -vapour.

Calculate fugacity coefficient for vapour & liquid

Calculate Kj= ratio of fugacity coeff. in liquid/ fugacity coeff. in liquid.

Iterate till convergence on Kj’s

Equation of State Based Equilibrium Calculations - Flowscheme

Danesh

Determination of Phase behaviour within Field Calculations Black Oil Model

Empirical correlations a function of (API Gravities, (P&T)

Compositional Models

Flash Calculations for each component.

K values either empirical or EOS based.

Heavy on computing needs.

Tendency to reduce components by defining a limited number of pseudocomponents, say 4 or 5.