The authors perform numerical simulation of a geothermal system and the interaction between a deep fault, lateral faults with a sandstone reservoir. The study aims to explain high observed temperatures in the Piesberg quarry, Germany using a sensitivity analysis around the fault and reservoir properties. My comments are mainly about clarification and publication is recommended after a minor revision.

Eq 1: Can you explain what Sm is? I assume it should be based on porosity, fluid density and their compressibilities and that you then can go from a time derivative of mass to a time derivative of pressure. However, is Sm then pressure dependent or assumed constant? Some definitions and assumptions should be given. You also seem to assume single phase.

What is the index m in qm?

Eq3 Does ‘effective’ also include the fluid?

The density should vary with temperature. Can you comment on how that was modeled?

175 Can the authors give the definition of Rayleigh number and its importance. What determines its value?

Table 1: Please add mathematical symbols for identification with the model parameters.

188 The kappa values have not been defined as far as I can see. What do they represent? What are the indexes MF and SST? If they correspond to values in table 1, the abbreviations should be listed there as well.

205 What is meant by ‘initial temperature’ in this case? Do you mean based on boundary conditions before flow is accounted for or simply an assumed geothermal gradient? Rather than ‘initial temperature’, do you not really mean ‘initial guess’ since you are only interested in the dynamic steady state? A thermal anomaly sounds to me a difference from an expected trend if the circumstances were as everywhere else, e.g. no faults etc. Is that what you mean?

Can you define mathematically how you define the initial state based on your main equations?

224 A mathematical definition of Pe number should be given earlier so it is clear how the parameters are combined.

In the figures showing temperature vs depth it would be good to include the observed anomaly of the Piesberg quarry one wants to explain since the sensitivity analysis can indicate which parameter is more likely to explain it. For example, figure 7 shows that a high fault permeability is needed to explain a high temperature. Is it within range? Alternatively you could discuss how your model explains the observations more quantitatively in 4.2. Can you state something certain about what is needed for such explanation? If the fault is needed, what properties must it at least have to realistically explain the observations? Which mechanisms or parameters are less important?

Review of the manuscript « Transport mechanisms of hydrothermal convection in faulted tight sandstones » by Guoqiang YAN et al., submitted to Solid Earth. December 2022. https://doi.org/10.5194/egusphere-2022-1185

This manuscript describes the possible fluid flow pathways within a paleo-geothermal system consisting of sandstones, a main fault, and transfer faults. Based on paleotemperatures indicating anomalously high values at a depth of 4.4 km, a numerical model of hydrothermal convection is presented. Unknown parameters (permeability values, anisotropy coefficient) are varied to reproduce the anomalous temperatures. I describe below some important points that have to be addressed. I detail after some minor points. The manuscript should thus be accepted for publication in Solid Earth, after accounting for the suggested revisions that I consider as « minor ».

Major comments

The adopted methodology is correct, but some pieces of information are missing. The authors used a numerical code for which basic information should be given. In particular, the chosen fluid density law must be specified. Indeed, the authors claim that their benchmark study successfully reproduced the Malkosvky and Magri (2016) experiment (line 176). However, in the Malkosvky and Magri study, a simplified density law (linear approximation) was used, and this approximation may not be valid for temperatures greater than 150°C. If the same simplified density law is used in the entire manuscript, then the results may be strongly biased, all the more that temperatures around 250-300°C are concerned. This point has to be clearly addressed. I suggest the authors to insert an Appendix in which the benchmark experiment would be described and illustrated.

Another important point deals with the basal thermal condition. The authors impose a basal heat flux of 0.1 W/m², which is much higher than the averaged continental value (67 mW/m²). The updated International Heat Flow database (e.g. Lucazeau, 2019 ; https://doi.org/10.1029/2019GC008389 ) indicates 2 surface heat flow values of 58 and 84 mW/m², at respectively 60 km SW of the area, and 42 km north of the area. There are no other HF values at smaller distances. The closest 100 mW/m² value is located 75 km west of the area (south-east Netherlands). This is not so important since using a lower basal heat flow would simply require increasing the permeability to get the same results, but this choice of 0.1 W/m2 must be discussed.

The authors use the Peclet number to qualify the heat transfer regime, which is ok, but what does mean « median Peclet number » ? At what depth is the Peclet number estimated ?

Minor points

• In the Abstract, the depth of 4.4 km should be indicated somewhere, maybe line 14.
• Line 70 : The word "anomaly" suggest that temperatures are greater than an expected value. What is this expected value, or, in other words, at what depth this reservoir was emplaced ? The range 270-300 °C may not be anomalous at a depth of 8 km for example.
• Line 70 : What is the uncertainty of this temperature range ? It should depend on the used methodology, but the authors should feed this part with more details on indirect paleotemperature data.
• Figure 1 and caption of Figure 1 are almost identical as in Wüstefeld et al, 2017. Should the authors need an authorization from the Marine and Petroleum Geology Journal ?
• Line 106 : We have here the answer for the depth of the thermal anomaly. This « 4.4 km » must be indicated before.
• Line 112. This sentence is too vague. The reader wants to know how the hypothesis of a Lateral Regional Flow has been elaborated. Is there any field observation for this flow ? Or is it simply a working hypothesis which will be investigated ?
• Line 130 : add : « and k is permeability (m²) »
• Line 133 (equation (3)) : The equation is wrong : each term of this equation should scale as W/m3, which is not the case in the 3rd term. In addition, radiogenic heat production seems to be neglected, whereas it is mentioned in the definition of the basal heat flux (l. 162). If the model was 1 km thick, neglecting heat production should be ok, but we have here a thickness of 12 km, and heat production should probably be accounted for.
• Figure 2. For clarity, I would also show the main fault in Figure 2b
• Line 167 : Topography is not accounted for. Is this hypothesis reasonable and why ?
• Table 1. « Compressibility » : Where does compressibility appear in the equations ? Is it the storage coefficient (same unit and related) ?
• Line 175 : It would be interesting to detail how the critical Rayleigh number is expressed as a function of the fault geometry, and how this « 61 » number is obtained.
• Line 449 : Germany.
• References : Several references are incomplete (e.g. the first one line 482 ; but also lines 498, 547, 549, etc)