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Abstract

This paper describes in detail computational techniques and formulations for constructing a phase envelope and/or subsequent isenthalpic/isothermal flash calculations that are practical for multiphase fluids in a non-isothermal environment.  These methods were designed especially for heavy oil applications and use in numerical simulators.  The methods are based on a fluid characterized by pressure and temperature dependent K-values.  Although these procedures may be extended to more general N-phase systems, the paper gives full details for a 3-phase oil/gas/water system.  Any number of hydrocarbon components may be present and water may exist as a liquid and/or a vapor.  The presence of non-volatile and/or non-condensable hydrocarbon components is treated.

Introduction

Reservoir simulators require a robust means to evaluate both the state of a multi-component, multi-phase fluid and the vapor-liquid equilibrium (VLE).  In contrast to black oil and compositional PVT calculations, thermal fluid VLE needs to account for water vapor.  It is common in thermal simulation to use correlated or tabular hydrocarbon component K-values which are dependent on pressure and temperature¹ rather than predict these from an EOS.  Although more limited in the range of pressure and temperature where the correlation or table is valid, i.e. away from meta-stable/critical regions and with non-complex fluids, the reduced functionality and monotonicity are valuable characteristics for robustness. 

Other methods exist for calculating thermal fluid VLE.  A thermodynamically rigorous method presented by Brantferger, Pope et al.² discusses a Newton-type entropy maximization algorithm combined with a Gibbs stability test to yield the number of phases.  Other methods include those discussed by Agarwal et al.³ which are based on successively calling a (P,T) flash in order to match a given total enthalpy, simultaneously solving an energy balance equation and Rachford-Rice equation and a hybrid of the above.

Algorithms discussed in this paper have been tested thoroughly in a new reservoir simulator⁴ over a number of years.  They are being used in a mass-variable based conventional and multi-segment well model and also in some circumstances to determine the state of reservoir grid cells.

Background of the Method

If sufficient heat is added to liquid water, it boils.  If more heat is added, then the liquid will disappear and all water will exist in a vapor phase.  If sufficient heat is added to a liquid water and oil mixture, it will also boil and at first three phases are formed.  Add more heat yet and one liquid phase will disappear.  If the oil is light such as a light olive oil or sewing machine oil, then the oil will probably vaporize first.  On the other hand if the oil is heavy and not very volatile then the water will boil away first.  If heat continues to be added to the system, all volatile liquid components will eventually vaporize.  If some components in the system are truly non-volatile, then there will always be a liquid phase whose presence is independent of the amount of energy in the system.  Similarly, if components are characterized as non-condensable, then a gas phase will always be present which contains these components.