Semi-Implicit Finite Volume Procedure for Compositional Subsurface Flow Simulation in Highly Anisotropic Porous Media
, Steven Velásquez 1,†, Nicolás Bueno 1,2,†, Juan David Valencia 1,†, Hillmert Alexander Solano 1,† and Juan Manuel Mejía 1,†Round 1
Reviewer 1 Report
The study described a numerical method to improve the order of accuracy and robustness of a numerical flow solver for porous media in the finite volume framework. The study is complete, the correction method is effective according to the authors statements, and the examples are interesting and meaningful.
The major defect of this paper, in my mind, is the lack of review and comparison of the correction methods from the previous studies. The author has stated in the introduction that ‘these methods were developed primarily for computational fluid dynamics (CFD) applications, and in most cases, porous media applications are limited to 2-dimensional geometries and simple single-phase fluid problems’. First, porous media application is a subtopic of CFD, I didn’t see why the correction methods developed for CFD do not apply to the porous media flow problems, at least from the description in this manuscript. I recommend Hrvoje Jasak’s phd thesis, ‘Error Analysis and Estimation for the Finite Volume Method with Applications to Fluid Flows’, for this topic. Secondly, there are numberless 3-dimensional multiphase simulations, the authors should be able to find good references without too much effort. I suggest the authors rewrite the introduction, and carefully evaluate the contributions of this paper compared to previous studies in this field.
There are other minor issues:
- The lack of the description of the correction of boundary conditions, which I think is the one of the main difficulties for porous media flow simulations.
- If possible, could the authors present a case to show the order of convergence before and after the correction? The x-axis would be the number of cells or the average cell size, and the y-axis can be the L-1 or L-2 norm.
- Please sort the references in the order which they are cited.
- Do a spelling check. E.g., p. 1, ‘prosous’ should be porous
- Figure 1 is redundant.
Author Response
We thank the reviewer for their careful revision of the paper, our response to the recommendations and corrections can be found in the attached file.
Author Response File: 
Author Response.docx
Reviewer 2 Report
In this work, the authors propose a semi-implicit procedure for general compositional flow simulation in highly anisotropic porous media as an extension of TPFA. This procedure accounts for non-orthogonalities by adding corrections to the residual in the Newton-Raphson method. The present semi-implicit formulation poses the guideline for FlowTraM implementation
for research and industry subsurface purposes. The authors validated FlowTraM with a non-orthogonal variation of the Third SPE Comparative Solution Project case. The present model is used to successfully simulating a real Colombian oil field. The idea of the paper is interesting and deserves publication. Similarities result of this paper is about 10% (see the attachment) and the paper is recommended for publications in the Fluid journal.
Comments for author File: 
Comments.pdf
Author Response
We thank the reviewer for their valuable insights.
Although no major corrections were provided by the reviewer, we improve the introduction according to their instruction.
Round 2
Reviewer 1 Report
- It is essential to show the convergence rate to confirm the effectiveness of the proposed method. Without too much work, the authors should be able to compare the results with that from the orthogonal mesh using much finer resolutions.
- Please highlight the changes from the original version before resubmission.
Author Response
Response to Reviewer 1 Comments
- It is essential to show the convergence rate to confirm the effectiveness of the proposed method. Without too much work, the authors should be able to compare the results with that from the orthogonal mesh using much finer resolutions.
R: The proposed recommendations were implemented. The results of the convergence rate study are shown in Figure 10 and the table 2 with the associated discussion.
- Please highlight the changes from the original version before resubmission.
R: The text edition is highlighted in blue.
The format was modified by request of the editor
Round 3
Reviewer 1 Report
I recommend acceptance of the manuscript.
