Summary
Use of multilateral wells for oil and gas production has gained strong
momentum in the past 5 years. However, most of the multilateral wells do not
deliver hydrocarbon fluids at expected production rates. One of the reasons for
this is that the well planners overestimate the productivity of wells by using
inaccurate methods for predicting composite-inflow-performance relationship
(IPR) of well laterals. A more-accurate method for predicting composite IPR of
multilateral wells is highly desirable. This paper fills the gap.
Starting from terms familiar to petroleum engineers, a general well model
was developed with consideration of reservoir-wellbore crossflow for lateral
IPR and coupling of fluid flow from individual laterals to the main wellbore.
The model allows different IPRs of laterals and permits crossflow between
laterals. Pressure losses in the vertical-, curvic- and horizontal-hole
sections are rigorously considered. Oil and gas wells are treated differently.
The modified Hagedorn-Brown correlation is used for modeling the flow in the
vertical sections, and the Beggs and Brill correlation is used for the curvic
and horizontal sections for oil wells. The Cullender and Smith method was used
for modeling the flow in gas wells. A computer simulator was developed based on
the model for predicting multilateral-well production rate. Case studies have
indicated excellent accuracy of the computer model. This work provides
petroleum engineers a reliable and user-friendly tool for designing and
evaluating multilateral wells.
Introduction
Although oil production by use of multiple-drainholes was reported in the
1960s (Borisov 1964), popular applications of multilateral wells for producing
oil and gas began in the early 1990s (Hardman 1993) after modern horizontal
drilling technology was developed. Salas, Clifford and Jenkins (1996)
identified eight categories of main potential applications of multilateral
wells. Vij, Narasaiah, Walia et al. (1998) provided an overview of the
multilateral technology and its limitations.
Raghavan and Joshi (1993) presented an analytical solution of well productivity
for symmetric horizontal radials defined as horizontal drainholes of equal
length kicked off from the same depth in symmetrical directions. The result was
an inflow equation (i.e., the effect of wellbore flow from sandface to the
common kick-off point was not considered). With a semianalytical solution,
Retnanto and Economides (1996) demonstrated the benefits of using symmetrical
multilateral wells in low- to medium-permeability reservoirs. Again, only
lateral-inflow performance was considered. Larsen (2006) presented closed-form
expressions of skin factors and productivity indices of radial-symmetric
multilateral wells. Wellbore hydraulics was not considered. Salas, Clifford and
Jenkins (1996) presented an IPR model for multilateral wells with the total
skin factor lumping the effects of reservoir homogeneity and other factors.
Wellbore hydraulics was also neglected. Wolfsteiner, Durlofsky and Aziz (2000)
developed a general and sophisticated model for productivity of nonconventional
wells in heterogeneous reservoirs. Wellbore hydraulics was not included in the
model. Yildiz (2002) presented a similar solution that also neglected the
effect of wellbore hydraulics. Yildiz (2005) compared his 3D multilateral-well
model with data from an electrolytic model and the Salas, Clifford and Jenkin’s
(1996) model. Good agreements were observed. Smith, Tweedie and Gallivan (1997)
addressed the importance of coupling the effects of fluid flow through
perforations and wellbore hydraulics in reservoir simulation for
multilateral-well economics evaluation. Permadi, Wibowo and Permadi (1998)
investigated the effect of wellbore hydraulics on inflow performance of a
stacked dual-lateral well, assuming single-phase flow in the wellbore. Ouyang
and Aziz (1998) presented a simplified approach to coupling wellbore hydraulics
and reservoir inflow for arbitrary well configurations. Chen, Zhu and Hill
(2000) presented another model of multilateral-well deliverability by
considering segmented horizontal holes and single-phase liquid flow in the
horizontal sections of the well. Kamkom and Zhu (2005) applied Vogel’s (1968)
two-phase flow correlation to multilateral wells. The absolute open flow (AOF)
was determined by use of Babu and Odeh’s (1989) horizontal-well IPR model. The
wellbore hydraulics was modeled with the correlation of Beggs and Brill (1973).
Kamkom and Zhu’s model is valid for reservoir pressures being lower than the
bubblepoint pressure. Although the hydraulics in the horizontal branches was
considered numerically, this is the first multilateral-well model that
considers hydraulics in all the wellbore sections. Ouyang and Huang (2005)
history-matched the oil production from a two-lateral well by coupling
reservoir inflow and wellbore hydraulics in a numerical simulator. The paper
does not describe how the hydraulics in the horizontal wellbore was
simulated.
In summary, most of the multilateral-well productivity models were derived on
the basis of mathematical analyses of fluid flow in the reservoir side, leaving
the flow inside the horizontal- and curvic-wellbore sections as a part of the
outflow performance of the well. A few studies have considered the wellbore
hydraulics in the horizontal section by assuming single-phase flow. Only one
study by Kamkom and Zhu (2005) addressed the wellbore hydraulics in the
horizontal and curvic sections. However, in reality, multilaterals are not
kicked off at the same point (i.e., kick-off points are separated by several
vertical sections). The hydraulics in these vertical sections is expected to
have more impact on well productivity than the hydraulics in the horizontal
sections. This is because the hydrostatic-pressure components that do not exist
in the horizontal sections will reduce well deliverability. No literature has
been found to address this issue. A more-accurate model considering hydraulics
in all the wellbore sections is highly demanded.
In this study, we define the upper-most conjunction as the end of inflow
system. We have derived a composite-IPR model by rigorously coupling the
wellbore hydraulics inside the well sections (i.e., vertical, curvic and
horizontal intervals) and the inflow models of all the laterals (lateral IPR).
Because the outflow from the upper-most conjunction is a well-known subject, it
is excluded from the scope of this paper although a multiphase-outflow model
has been incorporated in our computer program.
The composite IPR of both multilateral oil and gas wells were developed in this
study. Numerical results of these composite-IPR models were compared with that
of field wells, and a very good agreement was observed. This paper provides
petroleum engineers with a simple and accurate method for predicting and
evaluating performance of multilateral wells.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
29 May 2006
- Meeting paper published:
24 September 2006
- Revised manuscript received:
28 March 2007
- Manuscript approved:
9 October 2007
- Version of record:
20 May 2008
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