Comparative Solution Project

We have a question concerning the well condition on SPE11C.

In Page 23 of the last version of the description document (version 12 Oct.), it is written:

• "Note in particular that this implies that Well 2 is slightly longer than Well 1, which must be taken into account as the injection rates are given per well-length"  

and in Section 4.5 (Pages 24 – 25), it is specified:

• "As Well 1 is 3000m long, this corresponds to 𝑄1(𝑡)≈1.667⋅10E−2 kg/m⋅s(mass per length per time)".
• "As Well 2 is about 3002.6m long, this corresponds to 𝑄2(𝑡)≈1.665⋅10E−2 kg/m⋅s"

Do these mean that the flux (rate) is uniform along the well? If it is the case, this condition is different from the well models in commonly-used reservoir simulators, where the potential is generally constant along the well and the flux is not uniform. Different well conditions will provide different results. Could the CSP organisers give some comments? Thanks a lot.

Best regards,

Didier DING

Dear Ding, 

Thanks for your comment!  Indeed, you are correct that the well rates have been specified as constant along the length of the well. While we appreciate that this is perhaps not a standard option in some simulators (and may be contrary to well physics), I will try to explain the reasoning below. The co-organizers may of course have other thoughts. 

Firstly, it has been important for us to strive for a CSP description is precise enough that, at least in principle, there should exist a (unique) solution, so as to have a best possible basis to compare differences in the approximation and computational performance of the simulators. It turns out that in the presence of both mass and energy equations, containing both advective and diffusive processes (Darcy flux in addition to diffusion/dispersion for flow, and thermal conductivity for energy), rate based conditions are simpler to formulate precisely than potential-based conditions. This explains why both the well and boundary conditions are given in terms of rates. 

Secondly, we do not expect it to be possible to provide physically realistic well conditions (again in the presence of both mass and energy equations) without being significantly more detailed in the description of the well itself. Well modeling is an important topic in itself, and similarly to other aspects of CO2 storage not included in the study (notably hysteresis, geomechanics, geochemistry, etc.), the influence of realistic models for these processes, relative to the CSP as a common baseline, will be interesting topic to understand, and we would be happy to see contributions to the SPE Journal special issue along these lines.   

Finally, from a practical perspective, we believe that independently of what well models are implemented in various simulators, a constant flux along the well can be reasonably approximated by using a finite number of well segments of appropriate rates. In principle, this can be considered a numerical approximation, similar to the different representations of constitutive laws as either tables or expressions of elementary functions. Personally, I would expect that a reasonable approximation to a constant rate well can be achieved by a relatively low number of (independent) well segments (likely quite a bit coarser than the grid resolution in general), each injecting a prescribed rate proportional to their length.  

I hope these thoughts were clarifying, and feel free to follow up with additional questions!

Best regards, 

Jan