multivariate production systems optimization - Stanford University

The Orkiszewski gradient maps appear in Figures 7.8 and 7.9. Here the boundaries
between all four flow regions are very distinct. For more information on the multiphase
flow component used in this well model, see Chapter 3.
7.1.4 Developing the Choke Component
After the reservoir and flowstring components were completed, we next developed a
component to model the surface choke. A surprising degree of difficulty was encountered
at this stage. Recall from Chapter 4 that a surface choke is a binary device: it operates in
either critical flow or subcritical flow. Also recall that in critical flow the flow rate through
the choke is independent of the downstream pressure. Thus a discontinuity occurs at the
critical-subcritical flow boundary. Since the well model was to be used in an iterative
fashion, the surface choke component would have to be applicable to all flow conditions,
both critical and subcritical. Much to our dismay, we discovered after researching the
techniques available that although good correlations are available for single phase flow
across chokes, good correlations for multiphase flow across chokes are rare. Of the
correlations that are available, most are strictly for critical flow.
Nodal analysis handles the surface choke discontinuity by avoiding it. In nodal
analysis, the separator pressure is specified and then related to the pressure downstream of
the choke by a horizontal flow correlation. Then the pressure drop across the choke is
obtained by assuming that the choke is always in critical flow and using an empirical
correlation. Notice that by specifying the downstream pressure and then calculating the
upstream pressure, this procedure manages to determine both the upstream and
downstream pressures in critical flow. If we specified the upstream pressure and tried to
determine the downstream pressure during critical flow, the best we can do is to ascertain
the maximum downstream pressure.
Assuming that the choke is always in critical flow was rejected as an option for this
well model. An attempt was made to devise a method to handle both critical and subcritical
flow. One of the few correlations to make an attempt at modeling both critical and
subcritical flow is the Sachdeva et al. (1986) choke model. With a few modifications to the
algorithm, the Sachdeva et al. (1986) model was able to be incorporated into the well
model. During critical flow through the choke, the downstream pressure was determined
by assuming the choke to be at the critical-subcritical boundary. This assumption allowed
the critical pressure ratio to determine the downstream pressure. See Chapter 4 for details.
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