Two-Phase Thermal Simulation of Matrix Acidization Using the Non-Isothermal Darcy&ndash;Brinkman&ndash;Forchheimer Model

Wu, Yuanqing; Kou, Jisheng

doi:10.5194/egusphere-2025-4800

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https://doi.org/10.5194/egusphere-2025-4800

Preprints

13 Nov 2025

| 13 Nov 2025

Status: this preprint is open for discussion and under review for Geoscientific Model Development (GMD).

Two-Phase Thermal Simulation of Matrix Acidization Using the Non-Isothermal Darcy–Brinkman–Forchheimer Model

Yuanqing Wu and Jisheng Kou

Abstract. This study presents a comprehensive two-phase thermal model for simulating matrix acidization in porous media using the non-isothermal Darcy–Brinkman–Forchheimer framework. The model integrates multiphase flow, reactive transport, dynamic porosity evolution, and heat transfer, with temperature-dependent reaction kinetics incorporated through an Arrhenius-type formulation. A series of numerical experiments are conducted to investigate the effects of initial matrix temperature, injected acid temperature, and injection velocity on dissolution behavior and wormhole formation. Results show that the initial matrix temperature has minimal influence due to rapid thermal equilibrium, while high acid temperature significantly enhances reaction rates and promote localized wormhole growth. Verification experiments confirm that increasing acid temperature produces effects similar to decreasing injection velocity, as both shift the dissolution pattern from uniform to ramified and wormhole-dominated regimes. These findings offer valuable insights for optimizing acidizing treatments by balancing thermal and hydrodynamic conditions to improve stimulation efficiency.

Received: 30 Sep 2025 – Discussion started: 13 Nov 2025

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Yuanqing Wu and Jisheng Kou

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RC1:
'Comment on egusphere-2025-4800', Anonymous Referee #1, 16 Jan 2026 reply
I read the paper with interest. It presents a two-phase (oil and acidizing aqueous solution) thermal Darcy-Brinkman-Forchheimer (DBF) model for matrix acidization, incorporating temperature-dependent reaction kinetics. The related code is made available by the authors, which I did not try to compile and run myself. Key findings are claimed by the authors based on just seven 40x40 computed models with different initial or boundary conditions: the temperature of acid injection significantly affects dissolution patterns, while initial matrix temperature has minimal influence, and the imposed injection velocity plays also a role in shaping the dissolution pattern of the matrix.
Overall, the approach appears to be formally sound; however, in the present state the paper is seriously lacking some context as well as numerical applicability, and I cannot recommend it for publication without major-major revisions and integrations. I therefore recommend rejection prior to re-submission.
The formulation appears sound and it is adequately described too - in the sense that the assumptions and simplifications are clear and evident for the reader familiar with both reactive transport and with multiphase flow. Philosophycally, however, I have to admit that I would never advise to pursue a "global implicit" ADR model in this context, because no matter how complicated the model is made, it will be a very rough oversimplification in terms of chemistry and reactive transport, which are the controlling physical factors here.

Nothing is said about the implied formation matrix dissolved by acid injection. Is it a pure carbonate reservoir intended? What would change if there would be an inert matrix fraction, resisting to the acidification?

L 261: "rectangular matrix measuring 0.1 m × 0.1 m, discretized into a uniform grid of 40 × 40 cells": why has this particular length scale of 4 m been chosen? Anyhow, these numerical models can be taken as proof of concept for the validity of the formulation and of the numerical solution, but I am not convinced that such grid can be useful to depict real systems or draw meaningful conclusions about sensitivity of the process and the independence of the results from initial assumptions. Also, the images appear to be smoothly interpolated, hence misleading: a 40x40 image should be clearly "pixelated".

Line 266: "Porosity is spatially randomized with an average value of 0.18": how? Is it uniform white noise, or gaussian? Which range, which standard deviation? What happens if porosity is considered initially homogeneous?

Figure 1: I do not see any appreciable difference in the three pictures. I believe it is necessary to find some other way to summarize the results, highlighting the negligible effect of temperature. Maybe just picture their differences?

Figure 2-6: Same for Figure 1. At this point, figures 3 to 6 are redundant and the whole 4.1 section can be reduced to 1 figure for the lowest and highest temperatures, a mere proof of the negligible influence of the initial matrix temperature.

Figure 7: things start to be interesting, some effects are visible, but again only qualitatively and not quantitatively. However, from here on basically all color scales for the justaxposed images are not comparable anymore, which is not good scientific practice.

Overall, sections 4.2 and 4.3 stretch the results of two and three different model runs respectively, without any quantification which can be assumed to be transferable (thing such as scale invariance, transferability of results to higher temperature...) or usable otherwise. Moreover, most figures do not actually add anything meaningful to the paper. This is the case for example for figures 10 and 11 (only one among 4 would suffice), but also figures 12 and 14, are they not just the expected consequences of the imposed boundaries?

In my opinion, most of chapter 4 can be removed, hence highlighting the poorness of the presented results.

Generally speaking, the authors completely neglect the abundant literature about the use of Péclet and Damkohler numbers to describe these class of models and the interacting boundary and initial conditions. This is scientifically unacceptable in my opinion. Properly familiarizing with this well known literature - a good starting point would be the Golfier paper, cited by the authors, and following other works referencing it - will also inevitably lead to more convincing design of experiment for the paper. As the manuscript currently is, these are merely nice pictures without real usability.

The Kozeny-Carman relationships should be probably somehow bounded for very small porosity values.

I can go on and list further deficiencies of the present manuscript. Just to name a few which I would have expected:

1. lack of true control simulations, e.g. with initial homogeneous porosity;

2. lack of code efficiency evaluation, things such as required CPU-time for the seven simulation; scaling of the computations with more CPUs (the code is claimed to be parallel) and so on.

These aspects are in my opinion fundamental for the GMD journal and must be properly addressed for consideration

I stress the fact that the posed model - in the sense of equations and possibly their numerical implementation - could really be interesting and worth of publication, but at the moment I see no convincing results.

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Citation: https://doi.org/10.5194/egusphere-2025-4800-RC1

Yuanqing Wu and Jisheng Kou

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Short summary

Our study shows how heating up acid used in oil recovery can dramatically change the way it dissolves rock underground. While the natural temperature of the rock hardly matters, hotter acid speeds up reactions and carves more efficient flow channels. Interestingly, this has the same effect as slowing down the injection speed. These insights could help the energy industry design smarter treatments to boost oil production while using less acid.


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