Well Integrity Technical Section

This is something between a survey, a seed for a discussion and an attempt to reach out to people that the same niche obsession, namely modeling the mechanical behavior of cement.

If you model cement for work or passion, here are four questions for you:

• What software are you using? Commercial or open-source? Does it do non-linear elasticity/plasticity? Do you use contact problems? How about thermomechanics and poromechanics? Are most of your models plane strain or you have reasons for real 3D approaches?
• What bells and whistles have your cement constitutive models? Do you do plasticity? Viscoplasticity and viscoelasticity? Poroelasticity? If you switch constitutive laws on and off, what criteria do you use for each class of phenomena?
• Whether you go for full (visco)plasticity or simply impose a failure envelope, which yield surface do you use? Mohr-Coulomb, Cam-Clay, with/without cap?
• How do you calibrate your material parameters (elastic + failure + plastic)? Correlations? If you use lab tests, what do you take? Uniaxial compressive strength and one triaxial with confinement (after all, linear models like M-C only need two points ;-) )? Tensile/Brazilian tests? This question may abut proprietary or confidential recipes, so a lack of answers will be understood.

If this is not a one-person conversation (which, like tango, is best done in larger groups), I'll be glad to share my own answers to the questions above.

Thanks,

Hello Matteo,

I wrote a master's thesis on annular cement modeling - so my experience falls somewhere short of both profession and passion, but...

• I used Ansys Mechanical (commercial software - off the shelf). Ansys is more than adequate, with many non-linear elasticity models available. I incorporated specific energy based contact behavior. I did not (yet) incorporate thermomechanics, which has been a significant criticism. I built 3D models, which did not add much to any conclusions but did yield some beautiful graphics.
• I only briefly experimented with poroelasticity. The initial results did not apparently add much to my models, and I subsequently abandoned this consideration. As well as material parameters, I considered deviations from axial symmetry (i.e., hole ovality, formation mechanical anisotropy, and casing eccentricity). 
• I used the Mohr-Coulomb failure criterion. This resulted from considering research outside of the petroleum industry. More general cement models (i.e., from the mechanical and civil literature) suggested M-C is a common and adequate criterion. I found (probably not surprisingly) that the M-C predicted failure was overwhelmingly dominated by tensile stress.
• I calibrated most material parameters from SPE literature and previous work from our university's geomechanics lab. I considered confined compressive strength. I did design and execute an experiment to capture cement-steel bond behavior and estimate the bond strength as either shear strength or area specific energy (i.e., J/m2). The experiment showed the later parameter is appropriate at early set times. For the record, however, the models suggest that bond strength is not a comparatively significant factor in isolation failure. Predicted failure was, as previously mentioned, dominated by resultant tensile stress.

The experimental results (with parameter estimates) are currently being edited for possible publication. I'd love to hear your experience.

Also, though I'm a bit rusty, I can execute a passable tango.

Hello Douglas,

Now that we're a crowd, I'll add my personal answers to the questions:

• I use CalculiX, an open-source 3D FEM code, plus a bag of semi-analytic radially symmetric thermomechanical models in MATLAB. Non-linear behavior is very well treated by CalculiX and contact problem with linear elasticity also solve without glitches (plasticity+contact gives trouble, but mostly because of tensile failure while using Newton's method I think). The code can do thermomechanics easily, but I've mostly solved the problems with MATLAB for now: defining a plausible temperature profile for cement load cases requires attention and some experience. No poromechanics since I'm mostly concerned by cement behavior across an impermeable formation, cement permeability drops fairly quickly below 1 microD, and the time scale of pressure/temperature changes in most load cases is of the order of 1 hour (very short at low permeabilities). Cement is inherently plane strain, so I can think of very few cases where real 3D can add value. I'm not even sure deviated wells with stress anisotropy warrant a "fat" model.
• The constitutive model I use does (visco)elasticity/(visco)plasticity. I'm sure it should be relatively easy to introduce poroelasticity using similar field equations (say temperature or electrical current), but I haven't seen the need just yet.
• I find Mohr-Coulomb a bit too linear: it's OK for theoretical derivations, but concrete modeling upgraded to curved yield curves 30 years ago. The issue is that M-C overestimates tensile strength (so you have to "kink" the curve) and at high confinement the yield curve flattens out - more so with cement paste than with concrete. Instead of having three corrections (if we include the cap), I just took a relatively simple yield curve that passes through the reference tests and has a good asymptotic behavior. Then I glue a cap to account for pore crushing. There are 2-3 analytical models around, including Cam-Clay, but they are not particularly suited to cement.
• The bond behavior you mentioned is interesting: you certainly have bond with porous rocks (say, sandstone), but casing bonding is most probably an effect of radial stresses - temperature, shrinkage, formation creep or a combination of the three. So I don't use any specific energy for either interface. I use models for elastic properties and correlations for tensile and compressive strength. There are too few triaxial tests in the literature, and even fewer measured along the tensile meridian. Tests at high confinements are no more than 2 or 3. The approach works well for flavors of class G neat (more or less diluted), and should also work with concrete-like mixtures, even though I'd like to have better confirmation of compressive strength estimates and of the yield curve shape. Arguably, measuring compressive strength with a UCA is even worse than using a carefully crafted correlation: the only thing you measure is compressional wave speed, which is thrown into an unknown blender with three settings to produce UCS.