A model of pressure losses in perforated pipes that includes the influence
of inflow through the pipe walls compares favorably with past and recent
experimental studies. The single-phase model was developed in 1987, but it is
not generally known in the petroleum industry. This model is compared to three
experiments: one using air and two using water. The model must be manipulated
to conform with the way individual experimenters report their findings. In
general there is good agreement. Where there is poor agreement, the cause may
be experimental artifacts. A second model fails to match experimental results
when the pipe geometry changes significantly.
With the advent of horizontal drilling technology, flow in long perforated
pipes has become an important topic. Numerous investigations (Dikken 1990;
Penmatcha et al. 1997; Ouyang et al. 1998; Tang et al. 2000; Wolfstiener et al.
2000; Valvatne et al. 2001; Ouyang and Aziz 2001) have shown that pressure
losses in horizontal pipes and multiwell configurations significantly influence
the distribution of flow to the pipes. More flow enters the heel than the toe
of the pipe. While the influence of inflow through the pipe walls has been
recognized as an important effect, wellbore flow models used in these studies
either ignore the influence of perforations or use a flawed representation.
Recent experimental investigations (Ihara et al. 1994; Kloster 1990; Su 1996;
Yuan 1997; Yuan et al. 1999) of liquid flow in perforated pipes and channels
allow models of the influence of inflow on pressure losses to be tested for a
variety of pipe configurations. Agreement with experiments using air flow
(Olson and Eckert 1966; Yuan and Finkelstein 1956) can provide a strong
indication that a model developed with water is robust.
Numerous models of pressure losses within pipes with inflow exist. The three
investigated here are Ouyang (1998), Yuan et al. (1999), and Siwoń (1987). Only
Siwoń’s model compares favorably with all the experiments described in this
paper. I will concentrate on the comparison with Siwoń’s model, with some
review of the predictions using Yuan et al. The model of Ouyang does not have
the correct functional dependence. It is mentioned because it seems to be the
most widely used.
While Siwoń’s model is consistent with the experiments conducted by Olson
and Eckert (1966), Su (1996), and Yuan (1997), there are some data that do not
agree with Siwoń’s model. In this situation it is important to keep as much
transparency as possible so that readers can form their own opinions. The three
experiments are quite different, which provides a wide basis for comparison.
Unfortunately, the presentation of these data is also quite different. To
preserve the transparency of the original data, the models have been
manipulated to fit the original data presentation.
There are two basic conclusions: (1) Perforations cause an increase in head
gradient with and without inflow through the perforations; and (2) Inflow
causes larger head gradients than would occur without inflow, but 15% less
than would be expected, assuming a constant friction factor and considering
only the momentum increase induced by increasing flows.
The development starts with the momentum-balance equation—the basis for
understanding pressure losses in pipes. Three derivative forms of the balance
equation corresponding to different ways of presenting the experimental data
are presented. Next comes the model and experiments of Siwoń, followed by the
model of Yuan et al. Then, three experiments are described and compared to the
© 2006. Society of Petroleum Engineers
View full textPDF
- Original manuscript received:
30 November 2004
- Revised manuscript received:
3 March 2005
- Manuscript approved:
18 May 2005
- Version of record:
20 May 2006