Summary
This paper presents a mathematical model describing the variation of
temperature along the length of a horizontal well during the process of water
injection. The model is obtained from a theoretical treatment accounting for
both mass transfer and heat transfer between a horizontal well and a reservoir.
The treatment is 1D linear in the wellbore and 1D radial in the reservoir. A
numerical algorithm for reservoir temperature calculation is proposed and an
analytical solution is derived on the basis of some realistic assumptions. The
analytical solution can be used to generate the temperature profile in a
horizontal injection well for any assumed distribution of injection profile
along the length of the well, including injection profile that is uniform,
skewed toward the heel or the toe, or exhibits some discontinuity (e.g.,
leakoff into a high permeability streak or fracture). This paper also presents
comparison of temperature profiles obtained with the analytical solution given
in this paper and those obtained with a numerical reservoir simulator with
temperature option (ECLIPSE), which shows that the analytical solution yields
reasonable temperature propagation profiles along the wellbore. The effects of
injection rate and the injection profile are analyzed, and a quick in-situ
injection pattern-recognition method is proposed. Finally, examples are given
to show the practical application of the theoretical model.
Introduction
Use of horizontal wells for injection purposes is now commonplace. This is
because maturing fields produce increasing amounts of water, and horizontal
wells enable disposal of large volumes of fluid. Therefore, disposal objectives
can be met with a fewer number of wells. This is important in offshore
operations, in which well numbers are limited because of slot constraints on
the platform.
In terms of pressure maintenance, horizontal wells are also attractive. In
saturated reservoirs, in which voidage replacement is fundamental to achieve a
good recovery factor, horizontal wells help achieve injection volumes
commensurate with production volumes in the field. Therefore, they are
instrumental in reservoir management. Finally in terms of recovery, horizontal
wells are effective in achieving a good volumetric sweep, particularly in thick
reservoirs in which gravitational forces and stratification tend to undermine
sweep.
Measurement of injection profile in horizontal wells is also a common
requirement for assessing the efficiency of drilling or completion process,
cleanup or stimulation process, and injection or recovery process.
Injection profile in horizontal wells can be estimated with “production
logging” technology, but this may require coiled tubing to access the full
length of the well. Even with coiled tubing, there are practical limits of how
far the well can be logged (e.g., currently of the order of 1 to 2 km).
“Interventionless” means of determining the injection profile in horizontal
wells are therefore of interest to operators. A feasible interventionless
approach in horizontal wells is efficient completion designs for deployment of
the fiber optic line. There are published cases in the literature with fiber
optic-distributed temperature sensors deployed in horizontal wells. These are
deployed either through an extended tail pipe (i.e., “stinger” completion)
(Al-Asimi et al. 2002/2003), or through a groove in the sand screen.
The technology for measurement of distributed temperature on a periodic or
continuous basis is a well-established technology and has been widely applied
to reservoir and production monitoring (Brown et al. 2000, 2003, 2006; Laurence
and Brown 2000; Ouyang and Belanger 2006; Nath et al. 2007; Lee 2006; Johnson
et al. 2006).
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
15 July 2005
- Meeting paper published:
9 October 2005
- Revised manuscript received:
28 March 2007
- Manuscript approved:
20 May 2007
- Version of record:
25 February 2008
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