Thank you for the information and your question. Although you don't say specifically, I am assuming that your discharge states that your characterization of discharge is Other than Honorable, Undesirable, or something similar. If so, then although you can always submit a petition to the Army Board for Correction of Military Records, you would have a couple of hurdles to get past in order to be successful in your request.
The first is that there is a 15 year deadline for applying for an upgrade that can be waived by the Board but only if they find good cause for the delay. So, you would have to explain why your application was not sent within the 15 years. The next hurdle is actually the one you would have the most difficulty with. That is that the facts must show that the reason and/or the characterization of your discharge was made in error or was an injustice.
There is nothing in the facts that you shared that indicates anything that the Board would find fits this requirement. If you went UA more than once, the SPN code would fit. Your reason for going UA is not a defense to the UAs. In other words, going UA because a servicemember doesn't get the orders or location they want, is not defensible from a legal perspective. Again though, it is your right to apply and can find all the information you need, and the form, by going to the following link: http://arba.army.pentagon.mil/abcmr-overview.cfm
Please let me know if you need any clarification. If none is needed, if you could take a moment to leave a positive rating in the box above, I will receive credit for my work. Thank you.