Phase Envelopes From Black-Oil Models

Abstract

This paper compares the output of several available empirical black oil model correlations against compositional model results. In this process, the limitations of these models became apparent.

Even acknowledging the imperfections of black model implementation, it is possible to improve the quality of the outputs by means of making the definitions consistent and coherent across the prediction ranges.

A new method is outlined in order to extend the validity of the models in predicting both reservoir and multiphase flow simulations.

This new method is presented here and will be extended in a separated paper.

Introduction
The behavior of black oil fluid is commonly inferred from two PVT laboratory procedures: flash (or separator test) and differential liberation. Oil formation volume factor and gas solution ratios are calculated as explained by McCain. On the other hand, given a particular EOS is possible to obtain PVT fluid parameters by simulating the same laboratory procedures or making direct flash calculations at any particular condition.

The traditional calculation method outlined in 1 can be modified in a simple way to extend the validity of black oil model correlations by accounting the dew point curve. Negative gas solution ratios indicate liquid vaporization, and need not to be masked by any correction method. If we follow definitions literally, Rs diminish towards dew point and reaches a constant negative minimum at dew point and inside monophasic gas area. Oil formation volume factor can be lower than unity and in fact should be zero at dew point.

As modern calculations take into account both reservoir and multiphase wellbore and pipeline calculations, is of paramount importance to be able to accurately predict fluid properties in a wider range of pressure and temperature conditions.

The first objective of this paper is to make apparent the limitations of current PVT laboratory calculations and propose a revision.

A second objective is to present black oil model standard correlations phase diagrams together with phase diagrams calculated with EOS and acknowledge the differences and limitations of empirical correlations.

The third objective is to outline a new mathematical method to improve black oil correlations.

Definitions
The following definitions extracted from Dake will be taken as references:

• Rs. The solution (or dissolved) gas oil ratio, which is the number of standard cubic feet of gas which will dissolve in one stock tank barrel of oil when both are taken down to the reservoir at the prevailing reservoir pressure and temperature (units - scf. gas/stb oil).
  
• Bo. The oil formation volume factor, is the volume in barrels occupied in the reservoir, at the prevailing pressure and temperature, by one stock tank barrel of oil plus its dissolved gas (units - rb (oil + dissolved gas)/stb oil).
  
• Bg. The gas formation volume factor, which is the volume in barrels that one standard cubic foot of gas will occupy as free gas in the reservoir at the prevailing reservoir pressure and temperature (units - rb free gas/scf gas).

These parameters enable converting fluid volumes at any conditions to volumes at standard conditions.