There are various methods in place for determining the pressure losses that occur in flowing wells. It is not surprising that our prediction methods are not based on the exact solution of mathematical equations but rather on empirical or semi-empirical relationships. These relationships were developed by making certain assumptions about the applicable flow equations and then collecting data from a number of
correlations based on mathematical foundations and supported by observed field data.
Early theoretical work in vertical flow analysis was undertaken by Versluys (1930). This was followed by the first practical application proposed by Poettmann and Carpenter (1952). Other important contributions include the work of Gilbert (1954), Duns and Ros (1963), Hagedorn and Brown (1965), Orkiszewski (1967), Govier and Aziz (1972), and Beggs and Brill (1973). We refer you to volume 1 of Brown’s text (1977) to learn how each of the theoretical and practical developments of these individuals evolved. Let us here summarize the approach and the important contributions of each.
In reviewing these contributions we find it instructive to indicate the foundation of the work done, the pipe sizes to which the work applied, the fluids considered and, finally, to comment on the work of each.
Versluys’ work was theoretically based and described vertical flow patterns.
Poettmann and Carpenter’s work was semi-empirical and applied to 2-, 2 - and 3- inch tubing. The fluids studied were oil, gas, and water. They developed practical solutions for GLR less than 1500 scf/bbl and for flow rates greater than 420 BOPD. In 1954, Gilbert used field data to investigate flow in 2-, 2 - and 3-inch tubing. He investigated oil, gas, and water flowing wells and developed a practical set of
pressure profile graphs that can easily be used in the field by the engineer. Duns and Ros combined experimental laboratory work with field studies for all pipe sizes and all fluids to develop one of the best correlations for all flow rates. Hagedorn and Brown undertook both field and experimental work. They considered each of the three phases of flowing fluids in 1- to 4-inch tubing and produced a very useful generalized correlation for all ranges of flow rate. Orkiszewski reviewed all of the methods that had been published to that date and then, from his observations, prepared a single composite correlation. This correlation applies to all pipe sizes and fluids, and it may be used to predict pressure losses for all ranges of flow. It is widely used as the basis for computer programs in industry today. In 1972, Govier and Aziz, in Canada, published their correlations which were based on laboratory and field data for all pipe sizes and all fluids. Their correlations were based on a
mechanistic equation which had been tested against field data. In 1973, Beggs and Brill reported on the work being conducted at the University of Tulsa. They presented the results of laboratory studies on 1- and 1 -inch pipe for air and water. Their correlation handles all ranges of multiphase flow for any pipe angle. The practical application of this work is the prediction of pressure losses in inclined or directionally drilled wells. Many more correlations have been published and work continues today in this important research area.
The above-mentioned theoretical and empirical studies have left us numerous vertical pressure loss prediction methods, presented originally as correlations or pressure traverse curves. Brown for example, in volume 2a of his text, presented a full set of pressure traverse curves. Many computer programs have been written using one or more of their correlations to predict pressure losses during flow. The question remains as to which of these methods is most accurate under a given set of conditions. Statistical comparisons (Lawson and Brill, 1974) of several of the most
widely used methods have been undertaken in order to determine their relative accuracy over a broad range of variables and to identify the strengths and weaknesses of each technique.
No single pressure loss prediction method seems to be consistently superior under all ranges of production conditions. Comparisons of the methods of Poettmann and Carpenter, Duns and Ros, Hagedorn and Brown, Beggs and Brill, Govier and Aziz, and Orkiszewski show that the Hagedorn and Brown method has the best overall accuracy but that other methods perform better under different sets of variables and types of flow.
Despite variations in accuracy among the methods tested, they are within the range of engineering accuracy for use in sizing well equipment and designing artificial lift installations. Estimates of flow rates and bottomhole flowing pressures may also be made with reasonable accuracy by using these pressure gradient curves. The ones published by Brown or Gilbert may certainly be used with confidence. Your company may have its own internally published set of curves which you may choose to use. Many companies have computer programs that calculate pressure losses in tubing using a combination of the various correlations. These are quite accurate because they are generally written so as to use each correlation over its range of greatest accuracy.