Summary
Simplified analytical relations derived for homogeneous formations are
usually applied to the determination of the productivity of horizontal wells,
regardless of the presence of heterogeneities in the reservoir. Furthermore,
complex well architectures and the wealth of completion options currently
available cannot be taken into account properly because the well trajectory can
only be schematized as a single horizontal wellbore. However, the use of
numerical reservoir simulators to reliably forecast the productivity of
horizontal wells draining heterogeneous reservoirs may be time-prohibitive or
not feasible because of a lack of sufficiently detailed information, especially
during the appraisal phase or the early stages of production.
A new semianalytic technique is proposed in this paper to solve the inflow
equations in an approximate yet reliable manner. A solution to 3D problems of
single-phase flow into a horizontal well, taking into account friction in the
wellbore, is provided for both single-layer reservoirs and reservoirs
comprising two interfering layers. The method also has been extended to
describe the fluid flow when the well intercepts one or more fractures. The
presented technique allows very fast calculation of the well productivity in
oil and gas reservoirs, offering great flexibility in the placement and
architecture of the wells.
The method has been applied to two field cases for which the well
productivity under pseudosteady-state conditions was measured. One of these is
a 200-m-long horizontal well draining an isotropic carbonatic reservoir and
intersected by a natural low-conductivity fracture. The other is a similar
well, intercepting a natural high-conductivity fault, but the oil-bearing
formation is anisotropic. Good correspondence was found between the actual
productivity and the predictions obtained by application of the proposed
semianalytic technique.
Introduction
Horizontal wells are common practice in the present hydrocarbon industry,
and smart wells (including multilateral completions and wells with selective
access of different zones) are becoming increasingly commonplace. The modeling
of such wells is, in many cases, not ideal. Areas in which improvements are
welcome are well testing, well models in reservoir simulators, and fast models
for quick assessment of many field-development options. Further, the handling
of natural or hydraulic fractures is often suboptimal.
In reservoir simulation, fine grids need to be selected to properly capture
the flow behavior close to the well. Moreover, most reservoir simulators are
not equipped with extensive well models, which are required when friction in
the well becomes important or when two-phase flow develops in the well. This
situation has prompted the development of a number of analytical and
semianalytical tools, some of which are intended for implementation in a
reservoir simulator. Most of the first models, as well as many of the more
recent models, assume either constant influx density along the well or infinite
well conductivity in a single homogeneous layer. Dikken introduced the effect
of well conductivity for a single horizontal well in a homogeneous formation.
He started with the assumption that the flow is mainly perpendicular to the
wellbore, which allowed him to reduce the reservoir to a 2D flow domain,
coupled to a friction model in the well. Others followed this approach, but 3D
models were developed as well. A second kind of extension are the multilayer
models. Lee and Milliken and Kuchuk and Habashy used a method of reflection and
transmission, while Basquet et al. used a “quadrupole” method relating the
pressures between the various layers. The multilayer models are also, however,
still limited to constant-influx or infinite-conductivity wells.
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
17 March 2004
- Revised manuscript received:
20 December 2004
- Manuscript approved:
25 January 2005
- Version of record:
15 April 2005
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