Sometimes we do want to access the private project created by other users, e.g. when importing a model we get a private project conflict, to resolve this we have to find the project and delete it. If the owner of those projects are gone, we'll not be able to access them as normal, we'll have to do something unusual to get it.
Even though there're many different approaches to get this resolved in others' blogs/forum, I found my way is probably easiest. Here it is,
1. Find the AX database on sql server.
2. Open table ModelElement with the private project type only.The private project type is 38.
3. Change the prefix of the private project you are looking for from the original user Id to your user Id by a simple update like.
set Name = 'Admin_AOTExport2012_DynamicsPerfDirect'
where Name = 'JasonPAdmin_AOTExport2012_DynamicsPerfDirect' and ElementType = 38
4. Reopen AX client with your account, and you'll see the project appears in your private project