Summary
Current downhole measuring technologies have provided a means of acquiring
downhole measurements of pressure, temperature, and sometimes flow-rate data.
Jointly interpreting all three measurements provides a way to overcome data
limitations that are associated with interpreting only two
measurements--pressure and flow-rate data--as is currently done in
pressure-transient analysis. This work shows how temperature measurements can
be used to improve estimations in situations where lack of sufficient pressure
or flow-rate data makes parameter estimation difficult or impossible.
The model that describes the temperature distribution in the reservoir lends
itself to quasilinear approximations. This makes the model a candidate for
Bayesian inversion. The model that describes the pressure distribution for a
multirate flow system is also linear and a candidate for Bayesian inversion.
These two conditions were exploited in this work to present a way to
cointerpret pressure and temperature signals from a reservoir.
Specifically, the Bayesian methods were applied to the deconvolution of both
pressure and temperature measurements. The deconvolution of the temperature
measurements yielded a vector that is linearly related to the average flow-rate
from the reservoir and, hence, could be used for flow-rate estimation,
especially in situations in which flow-rate measurements are unavailable or
unreliable. This flow rate was shown to be sufficient for a first estimation of
the pressure kernel in the pressure-deconvolution problem.
When the appropriate regularization parameters are chosen, the Bayesian
methods can be used to suppress fluctuations and noise in measurements while
maintaining sufficient resolution of the estimates. This is the point of the
application of the method to data denoising. In addition, because Bayesian
statistics represent a state of knowledge, it is easier to incorporate certain
information, such as breakpoints, that may help improve the structure of the
estimates. The methods also lend themselves to formulations that make possible
the estimation of initial properties, such as initial pressures.
© 2010. Society of Petroleum Engineers
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History
- Original manuscript received:
4 August 2009
- Meeting paper published:
4 October 2009
- Revised manuscript received:
1 April 2010
- Manuscript approved:
24 May 2010
- Published online:
8 December 2010
- Version of record:
6 April 2011
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