Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling

Ruchi, Sangeetika; Dubinkina, Svetlana

doi:https://doi.org/10.5194/npg-25-731-2018

Articles | Volume 25, issue 4

https://doi.org/10.5194/npg-25-731-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/npg-25-731-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 25, issue 4

Research article

|

06 Nov 2018

Research article |

| 06 Nov 2018

Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling

Sangeetika Ruchi and Svetlana Dubinkina

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Final revised paper (published on 06 Nov 2018)
Preprint (discussion started on 23 Mar 2018)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'Comments on "Application of ensemble transform data assimilation methods for parameter estimation in nonlinear problems"', Anonymous Referee #1, 20 Apr 2018
- AC1: 'AC to Review 1', Svetlana Dubinkina, 12 Jun 2018
RC2: 'Comments', Anonymous Referee #2, 30 Apr 2018
- AC2: 'AC to Review 2', Svetlana Dubinkina, 12 Jun 2018

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Svetlana Dubinkina on behalf of the Authors (12 Jun 2018)

ED: Referee Nomination & Report Request started (04 Jul 2018) by Takemasa Miyoshi

RR by Anonymous Referee #1 (13 Jul 2018)

Suggestions for revision or reasons for rejection

[Comments to the Authors]
This manuscript compares performances of ETKF, ETPF with and without localization in parameter estimation experiments emulating underground subsurface modeling. In this revision, the authors provided sufficient descriptions to address the issues raised by reviewers; I feel the present manuscript was significantly improved from the first one. I still have several suggestions and concerns which would be helpful for improving further. Therefore, I would like to suggest this manuscript need minor revisions.

[Major Comments]
1. I wonder why ETPF can produce finer patterns of permeability field than ETKF (Fig. 8). Also, why does localization lead to spatially-coarser patterns (Fig. 15)? In the atmospheric data assimilation, the localization generally enables to obtain spatially finer patterns in analyses.

2. I became to wonder whether or the RMSE is a good measure to evaluate estimated fields. As shown in the results by ETKF, estimating spatially-smoothed fields would prevent terrible scores in RMSE. If authors can evaluate with an additional metric, it would be beneficial.

3. Is it allowable to tune the localization scale not for data misfits but for RMSE? If we think about realistic applications, such tuning of localization is not affordable.

4. I recommend revising Fig. 14 to contain two experiments (with and without localization) directly. It would be possible to remove Min/Max since they are not discussed here.

5. Readers would be interested a lot in how to choose ETKF or ETPF, and with or without localization. If authors could give some strategies (inferences), it would be very beneficial. Also, if there would be limitations or issues for realistic applications, please discuss them in the last section.

6. Title of the manuscript seems too broad

[Minor Comments]
1. Please revise the caption of Fig. 8.

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RR by Anonymous Referee #2 (02 Aug 2018)

Suggestions for revision or reasons for rejection

General comment
The new version of the manuscript is more clear than the previous one in terms of methodological aspects. The authors did a great job clarifying some methodological aspects and expanding the results presented in the paper. However there are some aspects that needs further improvement.
One important point that needs to be further clarified is what is the motivation to use ETPF in comparison with the classical IS for this particular application. In a few places in the manuscript the authors say that IS produce similar results in terms of the mean for the same ensemble size and initial ensemble.
There are also some presentation aspects that needs to be improved, I provide some examples below.

Minor points

Page 1, line 19 due to sampling error.

Page 1, line 24 leading modes instead of "first modes"?

Page 1, line 24 This approach is ... this sentence is not clear please rephrase it.

Page 7, line 4 introduce sampling errors ?

Page 11, line 10 The sentence starting with While for the parameter c ... is not clear. Please rephrase it.

Page 11, line 13, Figure 4 is introduced but the quantities shown here are disused in line 18 of the same page.

Page 11, line 14. In order to avoid any bias... may be better to say in order to increase the robustness of the results or in order to filter the sensitivity of the results to the initial parameter ensemble.

Page 11, line 20. Is there a way to know which method produce the best spread? Can the spread be compared to the estimation error to measure which method produce the best error / spread relationship.

Figure 4: It seems that both methods (ETKF and ETPF) have a bias in the estimation of parameters a, b and c. Is there a reason for that? Does IS also show that bias?

Page 11, line 21. The behavior of the estimated parameters with respect to their bounds is not clearly seen from Figs 3 or 4.

Page 12, It would also be interesting to see which parameter set produce a better estimation of the true pressure field. Parameter comparison alone is not conclusive since some parameters are better estimated by the ETKF and others better estimation by the ETPS, computing the error in P will help to decide which estimated parameter set produce the best results.

Figure 5 I suggest removing the 0 line from the figure legend.

Page 16, line 13, this means that ETPF sensitivity to the initial ensemble is due to the ...

Page 16, line 13. If IS produce the same result with the same ensemble size, what is the advantage of the ETPS in this application? It is important to provide a good motivation (which can be verified with the results) for using a more complex and computationally expensive technique.

Page 16, line 17. In Fig. 9 we plot the variance ...

Page 16, line 19. Why ETKF provides a smother variance? Is the variance estimation provided by the ETKF better or worse than the one provided by ETPF?

Figure 13, it seems that ETPF is more affected by sampling noise at small scales, so using a truncated representation of the fields significantly improve the results for ETPS. ETKF is more robust, it is probably filtering out the small scales (which are poorly observed and more difficult to retrieve) and because of this its performance is less affected by the truncation presented in this figure.

Table 1: In this table ETPS and ETKS are used instead of ETPF and ETKF. Note also that the optimal localization radius do not change much with ensemble size (usually in the ETKF the localization radius increases with the increase of the ensemble size eventually going to infinity).

Page 20, line 10. The sentence between parenthesis is not clear. How do the authors select the localization radius for each method?

For clarity the localized versions of ETPF and ETKF can be referred as LETPF and LETKF respectively.

Page 21, line 16. However , localization applied in the form of the ... I think that as long as the values of the parameters are within the required range the method achieves something interesting for parameter estimation (since parameter bounds are usually difficult to handle with other techniques like the EnKF).

Page 24, line 10. This conclusion also holds for the five parameter test case. From my point of view the results are not so conclusive in this case. An objective measure of the posterior error is missing in the discussion of the results.

Page 24, line 7. Another approach ... This approach also assumes that the log permeability can be represented as a Gaussian process. It is also not clear for me why the authors state that this approach is fully Bayesian?

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ED: Publish subject to minor revisions (review by editor) (21 Aug 2018) by Takemasa Miyoshi

AR by Svetlana Dubinkina on behalf of the Authors (24 Aug 2018) Author's response Manuscript

ED: Publish subject to minor revisions (review by editor) (14 Sep 2018) by Takemasa Miyoshi

AR by Svetlana Dubinkina on behalf of the Authors (21 Sep 2018) Author's response Manuscript

ED: Publish as is (17 Oct 2018) by Takemasa Miyoshi

AR by Svetlana Dubinkina on behalf of the Authors (18 Oct 2018)

Short summary

Accurate estimation of subsurface geological parameters is essential for the oil industry. This is done by combining observations with an estimation from a model. Ensemble Kalman filter is a widely used method for inverse modeling, while ensemble transform particle filtering is a recently developed method that has been applied to estimate only a small number of parameters and in fluids. We show that for a high-dimensional inverse problem it is superior to an ensemble Kalman filter.