Summary
The importance of pressure/volume/temperature (PVT) properties, such as the bubblepoint pressure, solution gas-oil ratio, and oil formation volume factor, makes their accurate determination necessary for reservoir performance calculations. An enormous amount of PVT data has been collected and correlated over many years for different types of hydrocarbon systems. Almost all of these correlations were developed with linear or nonlinear multiple regression or graphical techniques. Artificial neural networks, once successfully trained, offer an alternative way to obtain reliable results for the determination of crude oil PVT properties.
In this study, we present neural-network-based models for the prediction of PVT properties of crude oils from the Middle East. The data on which the network was trained represent the largest data set ever collected to be used in developing PVT models for Middle East crude oils. The neural-network model is able to predict the bubblepoint pressure and the oil formation volume factor as a function of the solution gas-oil ratio, the gas specific gravity, the oil specific gravity, and the temperature. A detailed comparison between the results predicted by the neural-network models and those predicted by other correlations are presented for these Middle East crude-oil samples.
Introduction
In absence of experimentally measured pressure/volume/temperature (PVT) properties, two methods are widely used. These methods are equation of state (EOS) and PVT correlations. The equation of state is based on knowing the detailed compositions of the reservoir fluids. The determination of such quantities is expensive and time consuming. The equation of state involves numerous numerical computations. On the other hand, PVT correlations are based on easily measured field data: reservoir pressure, reservoir temperature, oil, and gas specific gravity. In the petroleum process industries, reliable experimental data are always to be preferred over data obtained from correlations. However, very often reliable experimental data are not available, and the advantage of a correlation is that it may be used to predict properties for which very little experimental information is available. The importance of accurate PVT data for material-balance calculations is well understood. It is crucial that all calculations in reservoir performance, in production operations and design, and in formation evaluation be as good as the PVT properties used in these calculations. The economics of the process also depends on the accuracy of such properties.
The development of correlations for PVT calculations has been the subject of extensive research, resulting in a large volume of publications.1–10 Several graphical and mathematical correlations for determining the bubblepoint pressure (Pb) and the oil formation volume factor (Bob) have been proposed during the last five decades. These correlations are essentially based on the assumption that P b and Bob are strong functions of the solution gas-oil ratio (Rs) the reservoir temperature (T), the gas specific gravity (?g) and the oil specific gravity (?o) or
P b = f 1 ( R s , T , γ g , γ o ) , ( 1 )
B o b = f 2 ( R s , T , γ g , γ o ) . ( 2 )
In 1947, Standing1 presented graphical correlations for the determination of bubblepoint pressure (Pb) and the oil formation volume factor (Bob) In developing these correlations, Standing used 105 experimentally measured data points from 22 different crude-oil and gas mixtures from California oil fields. Average relative errors of 4.8% and of 1.17% were reported for Pb and Bob respectively. Later, in 1958, Lasater9 developed an empirical equation based on Henry's law for estimating the bubblepoint pressure. He correlated the mole fraction of gas in solution to a bubblepoint pressure factor. A total of 137 crude-oil and gas mixtures from North and South America was used for developing this correlation. An average error of 3.8% was reported. Lasater did not present a correlation for Bob In 1980, two sets of correlations were reported, one by Vasquez and Beggs10 and the other by Glasø.7 Vasquez and Beggs used 600 data points from various locations all over the world to develop correlations for Pb and Bob. Two different types of correlations were presented, one for crudes with °API>30 and the other for crudes with °API 30. An average error of 4.7% was reported for their correlation of Bob Glasø used a total of 45 oil samples from the North Sea to develop his correlations for calculating Pb and Bob. He reported an average error of 1.28% for the bubblepoint pressure and ?0.43% for the formation volume factor. Recently, Al-Marhoun4 used 160 experimentally determined data points from the PVT analysis of 69 Middle Eastern hydrocarbon mixtures to develop his correlations. Average errors of 0.03% and ?0.01% were reported for Pb and Bob respectively. Dokla and Osman6 used a total of 50 data points from reservoirs in the United Arab Emirates to develop correlations for Pb and Bob. They reported an average error of 0.45% for the bubblepoint pressure and 0.023% for the formation volume factor.
The conventional approach to develop PVT correlations is based on multiple-regression techniques. An alternative approach will be to use an artificial neural network (ANN). PVT models based on a successfully trained ANN can be excellent, reliable tools for the prediction of crude-oil PVT properties. The massive interconnections in the ANN produces a large number of degrees of freedom, or fitting parameters, and thus may allow it to capture the system's nonlinearity better than conventional regression techniques. Recently, artificial neural networks have found use in a number of areas in petroleum engineering.11–20 The objective of this study is to use ANNs to develop accurate PVT correlations for Middle East crude oil to estimate Pb and Bob as functions of Rs, T, ?g, ?o. With additional experimental data, the neural-network model can be further refined to incorporate these new data. In addition, in this article we evaluate the accuracy of the ANN models developed in this study compared to other PVT correlations.
A New Oil Formation Volume Factor Correlation of Egyptian Crude Oils