multivariate production systems optimization - Stanford University

more stable than unmodified Newton’s Method, and was to optimize long-term financial
objectives.
7.1.2 Developing the Reservoir Component
To replicate the reservoir dynamics and inflow performance in the well model, this study
adopted a reservoir model developed by Borthne (1986) at the Norwegian Institute of
Technology, as discussed in Chapter 2. The reservoir model was originally designed with
just this purpose in mind--to provide a simple but functional reservoir component to be
included in a larger model. The model provides an accurate representation of constrained
reservoir performance that requires minimal computer processing. Borthne’s model is a
black-oil model that performs a generalized material balance calculation in concert with an
inflow performance relationship based on pseudopressure. The reservoir model is
constrained by both pressure and flowrate. In addition to specifying a minimum flowing
well pressure, two flowrates must be specified: a minimum flowrate and a maximum target
flowrate. The model attempts to satisfy the target flowrate without violating the minimum
flowing well pressure. For more details on the reservoir component used in the well
model, see Chapter 2.
7.1.3 Developing the Tubing Component
The next stage in the model development was to design and develop a component to model
the multiphase flow through the vertical flowstring. For this we relied on the many
empirical correlations that have been developed over the years. Three correlations were
selected to be included in the model. These were the modified Hagedorn & Brown
correlation (1965), the Orkiszewski correlation (1967), and the Aziz, Govier, and Fogarasi
correlation (1972). All three correlations are extensively used in the petroleum industry.
The Hagedorn and Brown (1965) correlation is one of the most empirical available, the
Aziz et al. (1972) correlation has the strongest theoretical basis.
Gradient maps of the three correlations were generated and are shown in Figures
7.4 through 7.9. Figures 7.4 and 7.5 show the gradient surface generated by the modified
Hagedorn and Brown (1965) correlation. The transition from the original Hagedorn and
Brown correlation, representing slug flow, to the Griffith & Wallis (1961) correlation,
representing bubble flow, is very distinct. Figures 7.6 and 7.7 show the Aziz et al. (1972)
correlation with their suggested flow map superimposed. Note theat the map appears
continuous everywhere except at the boundary between bubble flow and slug flow.
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