Batch processes usually have some input data, some processing, and some output data. And often these things cover most of the functional requirements of a batch process. So I see nothing which is not easily doable by using Excel:
For a good high-level view, I would recommend using data flow diagrams. This gives a good overview about the system's structure and how different processes are dependent on each other (note Excel's drawing capabilities are quite sufficient for this). Data flow diagrams are especially helpful when you have multiple batch processes to describe, or when you have a batch process which can be splitted up into several partial processes.
For the description of the processes themselfes, you can use high-level pseudocode, and/or verbal descriptions. You will use Excel as a text editor here, maybe with some formatting options for headlines. It is not the ideal tool for this, but often sufficient. You could also try to draw some activity diagrams with those drawing tools, but in my opinion, these don't give you enough "bang for the buck" - lots of effort to draw them for something which can be described in some pseudocode much quicker, in a much more comprehensive way.
You may need to give some representative examples for the input and output data. If this data has tabular structure, that should be a no-brainer in Excel.
Non-functional requirements can be described in a simple two-column table as well: one column for the type of requirement, and one for the spec (like "performance - should not last more than 10 minutes", or "compatibility - must be compilable with C++11 since we have to support older compilers for system XY"). So nothing which cannot be done easily with a spreadsheet.
the requirements become quite unreadable when there are many ways for the process to go
You need to figure out how to break down the processes into smaller, manageable parts, that is one of the main tasks in requirements analysis. This is not a problem a tool can solve for you, neither Excel nor any other tool.
Of course, all of the steps I mentioned can be done in a word processor like MS Word as well, some of them probably better. But if you have serious problems to create a readable in spec in Excel, you will encounter the same problems using Word.