Summary
A method is presented for estimating the distribution of a parameter related
to the productivity index along the length of a liner-completed horizontal
well, using measurements of well flowing pressure at multiple points along the
path of flow in the wellbore. This is the concept of near-wellbore diagnosis
with multipoint pressure measurements, which in principle can be made with
fiber-optic sensors. The deployment mechanism of the sensors is not modeled in
this study, although the temperature version of such sensors has been deployed
in horizontal wells on an extended-tail-pipe or stinger completion. (The
temperature sensors also have been deployed in horizontal wells with
sand-screen completions, in direct contact with the formation, but that
configuration is not investigated in this study.)
The parameter that is estimated is known in reservoir-simulation terminology
as the connection factor (CF), which represents the hydraulic coupling or
connectivity between the reservoir and the wellbore (between formation
gridblocks and well segments). Parameter CF has units of md-ft, similar to flow
capacity, or productivity index multiplied by viscosity. Specifically, the
parameter is directly proportional to the geometric mean of the permeability
perpendicular to the horizontal axis of the well and is inversely related to
skin. No attempts are made in this study to estimate these parameters
individually, which may require recourse to other methods of well diagnosis
(e.g., dynamic formation testing, transient analysis, and production
logging).
The method applies to flow under constant-rate conditions and yields
estimates of the CF, which represents the quality of the formation in the
vicinity of the well and the integrity of the completion along the well
trajectory.
The quality of the inversion is determined by the spatial density and
accuracy of the multipoint measurements. Inversion quality also depends on
knowledge of the wellbore hydraulic characteristics and the relative
permeability characteristics of the formation. The basic configuration
investigated in this study consists of a five-node pressure array in a 2,000-ft
horizontal well experiencing a total pressure drop of approximately 60 psi when
produced at 10,000 STB/D. A reasonable estimate of the distribution of the
parametric group CF is obtained even when allowing for measurement drift and
errors in liner roughness and relative permeability exponent. Also, the
inversion can be rendered insensitive to knowledge of the far-field
permeability through a scaling technique. Therefore, good estimates of the
near-wellbore CF profile can be obtained with uncertain knowledge of the
reservoir permeability field. This is important because the technique can be
applied not only to early-time but also to late-time data. The application of
the multipoint pressure method is illustrated through a series of examples, and
its potential for near-wellbore formation evaluation for horizontal wells is
described.
Introduction
Horizontal wells can be diagnosed on the basis of information derived from
openhole and cased-hole surveys. These include petrophysical logs, dynamic
formation testers, production logging, and pressure-transient testing. With the
advent of permanent sensing technologies and the development of methods of
production-data inversion or history matching, a new form of cased-hole
diagnosis can be envisaged, with improved spatial and temporal coverage and
without the need for in-well intervention and interruption of production. The
impact of such methods on reservoir-scale characterization can also be
significant.
There are two main preconditions for the development of such a methodology,
one concerning sensing technology and the other concerning interpretation
methodology. Permanent sensing technology has made great progress during the
last decade, with the development of single-point and distributed measurements
that can be deployed with the completion (pressure, flow rate, and distributed
temperature). However, these systems are typically developed as standalone
measurement units and do not enjoy the required degree of integration. Current
modeling methods, however, can be used to provide an incentive for such
integration.
The well-diagnosis problem is decoupled in our investigation into diagnosis
of flow condition in the wellbore and diagnosis of near-wellbore formation
characteristics. (By “near-wellbore,” we mean the wellbore gridblock scale.)
This is partly to adhere to the conventional demarcation between production
logging and dynamic formation evaluation and partly to show the natural
consequence of the mathematical problem. Basically, the wellbore-diagnosis
problem (determination of flux distribution, as in production logging) can
treat the formation simply as a boundary condition, but the
formation-evaluation problem cannot do the same (i.e., treat the wellbore
interface as a boundary condition) because evaluation is based on measurements
made inside the wellbore. Thus, both the wellbore and the formation have to be
taken into account. (Sensors that are in direct contact with the formation, as
mentioned in the Summary, are emerging.8 Therefore, the evolution of this
problem is to be expected.) In this study, the permanent or in-situ analog of
dynamic formation evaluation is investigated. The in-situ analog of production
logging is investigated in a parallel study.
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
3 May 2004
- Revised manuscript received:
8 April 2005
- Manuscript approved:
25 June 2005
- Version of record:
15 October 2005
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