Dear all,

Thank you all for a very productive meeting before Easter. We were very impressed by the quality and quantity of early submissions, and the good discussions we had on our virtual workshop. Some of you asked if there would be another such early submission and virtual workshop, and we believe this is a good idea.

**Therefore, we are working towards a "second early submission deadline" on June 1**^{st}, with a virtual workshop in mid-June. As in March, this deadline is completely voluntary, but we hear from you that the early submission was a good opportunity to focus your work and get feedback on how the community was developing. Our goal is also to have pre-submission validation scripts ready well in advance of this second submission deadline. More details on this will be forthcoming in a later communication.

Both before and during our last virtual workshop, we received feedback from several of you, the answers to which we have collected here.

Change to the CSP description:

__Reporting digits for time and pressure for case 11A and 11B__.
- The sparse reporting of pressure in 11A should be increased from four to six significant digits.
- The sparse reporting of time in 11B should be increased from four to five significant digits.

Clarifications:

__Pressure reporting in wells__: The __water pressure__ should be reported in the pressure field in the sparse data.
__Submission data structure__. As was discussed, the final SPE11 submissions may contain more than 100k files, and it is imperative that these can be processed automatically. Several of you already uploaded your pre-submission according to the specifications, however, some of you missed various specifications. Attached are some remarks from Bernd's slides. Also, please note that several of the scripts used to process the data are already openly available on github (https://github.com/Simulation-Benchmarks/11thSPE-CSP), so that you can test the conformity of your results to the development of the evaluation scripts. Moreover, we will work on getting a "presubmission check" script available well before the final submission deadline, and will communicate this when it is ready.
__Frequency of sparse data reporting__. A concern was raised that the frequency of sparse data reporting prohibited long time-steps. We emphasize that regarding both spatial grids, as well as time-steps, the participants should use their own best judgement, independent of the reporting requirements. If this leads to longer time-steps than the reporting times (or larger/smaller grid sizes), feel free to use any interpolation you deem appropriate to report results at the stated reporting times.
__Thermodynamics__. A concern was raised that the CSP description states that the internal energy should be considered independent of composition. This has the effect that mixing of CO2 and brine becomes somewhat more exothermic than if a (more realistic) mixing rule would be implemented. However, based on preliminary calculations, impact on the results in CSP11 simulations appears to be small, and this simplification therefore appears to be comparable to many of the other physical simplifications chosen in the description. However, it may be that the computational difficulty will depend on the thermodynamical modelling, although this cannot be stated with certainty. Thanks to Olav Møyner and Halvor Nilsen at SINTEF Digital for extended discussions, and testing, on this topic.
__Specification of injection well__. The CO2 injection is specified in terms of the temperature of the injected CO2. A question was raised as to why not use enthalpy? This is a fair question, and the specification could well have been given in enthalpy. We remark that the injection temperature specified is below what is likely to be seen on the Norwegian Continental Shelf, but may be realistic in other cases. The resulting region of negative buoyancy of CO2 is an interesting part of the parameter regime, that has been discussed in various feasibility studies regarding CCS, and is interesting to conduct a comparative study of.
__Immobile saturations__: There are two ways to define immobile saturations, depending on whether one considers only the CO2 that is currently immobile, or the fraction of mobile saturation that will be immobilized due to future migration. Given the importance of dissolution in the context of the CSP, we deem the "future immobile" saturation as less relevant, and the CSP description therefore specifies in "immobile free-phase CO2" as "CO2 at saturations for which the nonwetting relative permeability equals zero".
__Evaluation of fingering__: The fingering metric provided as equation (17) has created some questions. This is a regularization of "surface area", relatively well known in mathematics in the context of level sets and phase-field models (see e.g. references [1] and [2] below). In our context, the fingering metric of equation (17) therefore effectively captures a measure of "average fingering relative to a flat surface". It has units of length in 2D and units of area in 3D. A similar metric would be to calculate the area of some contour surface, but due to the variations in CO2 concentration in water, it is unambiguous how to choose a representative contour value. A sample script for evaluating this metric on the reporting grid is available on github, however, it will most likely be significantly more accurate to calculate this quantity on the computation grid. The concentration is normalized by the solubility limit (not the maximum concentration over time), and the absolute value of a vector is its Eucledian length.
__Well pressure during equilibration__. After equation (26) of the CSP description, the pressure at the center of well 1 is given. We emphasize that this is in the context of the initial condition, i.e. the pressure should be prescribed at -1000y, and not considered as a "constant pressure well" during the equilibration period.
__Github utility development group__. If you want to contribute to the development of community resources for the SPE11, the Utility Development Group meets every last Thursday of each month at 17:00 CET. Everyone is welcome to join: https://unistuttgart.webex.com/unistuttgart-en/j.php?MTID=meaab3eae60cea151746685a6b21a4ca4

Thanks again to all,

Best regards,

Jan M. Nordbotten

Martin Fernø

Bernd Flemisch

Anthony Kovscek

Knut-Andreas Lie

[1] De Giorgi, E. Su una teoria generale della misura (r − 1)-dimensionale in uno spazio ad r dimensioni. Annali di Matematica 36, 191–213 (1954)

[2] Modica, L. "The gradient theory of phase transitions and the minimal interface criterion." Archive for Rational Mechanics and Analysis 98 (1987): 123-142.