Summary
This paper presents an analytic model for computing the
wellbore-fluid-temperature profile for steady fluid flow. Although wells with a
constant-deviation angle can be handled with existing analytic models, complex
well architectures demand rigorous treatment. For example, changing
geothermal-temperature-gradient and deepwater wells present significant
challenges. Additionally, available analytic models rarely provide calculation
methods for various required thermal parameters, such as the Joule-Thompson
(J-T) coefficient and fluid expansivity.
The approach taken in this study entails dividing the wellbore into many
sections of uniform thermal properties and deviation angle. The governing
differential equation is solved for each section, with fluid temperature from
the prior section as the boundary condition. This piecewise approach makes the
model versatile, allowing step-by-step calculation of fluid temperature for the
entire wellbore. We present simple, thermodynamically sound approaches for
estimating thermal parameters.
Success is indicated when performance of the proposed model is compared with
data from three wells, producing two-phase gas/oil mixture, single-phase oil,
and single-phase gas. Sensitivity of the estimated fluid temperatures to
various thermal properties is also examined with our model. Overall, the
effects of the J-T coefficient and liquid expansivity are found to be
significant.
Introduction
Modeling fluid-temperature and density profiles in wellbores is crucial for
the design of production tubulars and artificial-lift systems, gathering
pressure data for real-time reservoir management, and estimating flow rates
from multiple producing horizons with distributed-temperature sensors.
Significant advances have occurred in wellbore-fluid-temperature modeling
since the pioneering work of Ramey (1962). Ramey’s work addressed single-phase
flowing-fluid temperature in a line-source well. In this regard, models of
Alves et al. (1992), Sagar et al. (1991), and Hasan and Kabir (1994) are worthy
of note. In particular, these models extended application to two-phase flows.
Yet, the available analytic models are inadequate for direct application to
modern directional wells that traverse formation with significantly varying
thermal properties with multiple changes in deviation angles. In such cases,
even the simple task of estimating geothermal temperature as a function of
measured depth (MD) becomes nontrivial. Obviously, geothermal gradient strongly
influences heat loss of wellbore fluids, requiring careful piecewise
computation. The solution presented in this paper addresses these issues and
lends itself to user-friendly spreadsheet computations, if one so chooses.
© 2009. Society of Petroleum Engineers
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History
- Original manuscript received:
1 August 2007
- Meeting paper published:
11 November 2007
- Revised manuscript received:
26 February 2008
- Manuscript approved:
12 March 2008
- Published online:
1 May 2009
- Version of record:
1 May 2009
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