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Pressure up tapered casing and set packer

Pressure up tapered casing and set packer

Pressure up tapered casing and set packer

Hi all,
I have come across a wee problem that has really got me scratching my head. Not only because I cant solve it, but I can't even think on where to start for a reference.
I have a casing string that will have a casing packer set behind it. The casing string is tapered from 10.75" to 9.625". The packer is initiated/ inflated by pressuring up the casing internally. The packer is at the 9.625"  depth. My issue is, when pressuring up the casing, I induce a force and thus stress into the casing string due to the internal shoulder (10.75" to 9.625"). When the packer sets, this force is locked in to the casing when the pressure is removed. The casing is fixed top and bottom by the way.
Problem is, when the pressure is applied, I have a different force in the 10.75" compared to the 9.625" casing. I want to know what the resultant force in the entre section is when the pressure is bled off.
Is there an easy way of looking at this? Any pointer towards a decent reference would also be highly appreciated.
I have attached a drawing for reference.
I use Landmark's WellCAT quite a lot for performing most of my casing and tubing analysis. However, it is on bespoke designs like this that revert us back to paper. WellCAT cannot model casing packers unfortunately. I've tried many a workaround to attempt to get a better understanding of how to approach this but unfortunately on this occasion I am hitting a brick wall.
Let me know if you need any other details.

Thanks in advance


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