Summary
With recent advances in permanent downhole technology, well-test analysts
now have to deal with enormous amounts of data. Using these data requires the
development of efficient algorithms that are able to extract the relevant
information from the data at minimal cost. We present a multiresolution wavelet
approach to estimate the spatial distribution of reservoir parameters, by
performing the nonlinear least-squares regression in the wavelet domains of
both time and space. Wavelet transforms have the ability to reveal important
events in time signals or spatial images. Thus, we transformed both the model
space and the time-series pressure data into spatial wavelet and time wavelet
domains, respectively, and used a thresholding to select a subset of wavelet
coefficients from each of the transformed domains. These subsets were used
subsequently in nonlinear regression to estimate the appropriate description of
reservoir parameters. The appropriate subset is not only smaller; the problem
is also reduced to the consideration of only the important components of the
measured data and only the part of the reservoir description that depends on
them.
As a test of the approach, we first applied the model to well-test problems
involving 1D (radially composite) reservoir systems. The inverse problem was
solved to estimate the distributed permeability values by performing the
nonlinear least-squares regression in the wavelet domains (time and space).
Results obtained were compared with those obtained from the conventional
nonlinear-regression approach, using all the pressure-time data and the full
set of spatial reservoir parameters. The time/space wavelet approach proved to
be efficient. By reducing the dimensions of the model and data spaces, the
approach eliminates redundancy in the reservoir description and in the data
set. Significantly, the approach reveals the true number of reservoir
parameters that can be appropriately estimated from a given data set and also
reveals which components of the full data set are active in constraining the
reservoir model. Thus, the approach provides a good means to integrate
different data properly while avoiding the inclusion of irrelevant data during
nonlinear regression.
© 2011. Society of Petroleum Engineers
View full textPDF
(
1,133 KB
)
History
- Original manuscript received:
19 January 2010
- Meeting paper published:
22 September 2008
- Revised manuscript received:
1 January 2011
- Manuscript approved:
25 January 2011
- Published online:
24 May 2011
- Version of record:
7 June 2011
View Cart
